LiAuto-DSR/GeoGramBench huggingface dataset:
A solid figure has a surface area of 54105(mm)^2.

What must the height $h$ mm of the solid figure be?

Round your answer to the nearest whole number.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 radius = 20
 height = 70
 
 theta = np.linspace(0, 2*np.pi, 100)
 x = radius * np.cos(theta)
 y = radius/2 * np.sin(theta)
 
 fig, ax = plt.subplots(figsize=(5,8))
 
 ax.plot(x, y + height, 'k')
 
 ax.plot(x[:50], y[:50], 'k--')
 ax.plot(x[50:], y[50:], 'k')
 
 ax.plot([radius, radius], [height, 0], 'k')
 ax.plot([-radius, -radius], [height, 0], 'k')
 
 ax.annotate(
     '', xy=(radius + 4, height), xytext=(radius + 4, 0),
     arrowprops=dict(arrowstyle='-', lw=1.5)
 )
 ax.plot([radius+3, radius+5], [height, height], color="black")
 ax.plot([radius+3, radius+5], [0, 0], color="black")
 ax.text(radius + 6, height/2, '$hmm$', va='center', fontsize=12)
 
 ax.annotate(
     '', xy=(0, height+0.5), xytext=(-radius-0.5, height+0.5),
     arrowprops=dict(arrowstyle='-', lw=1.5)
 )
 ax.plot([0, 0], [height-0.2, height+1.2], color="black")
 ax.plot([-radius, -radius], [height-0.2, height+1.2], color="black")
 ax.text(-radius/2, height + 1, '$79mm$', ha='center', fontsize=12)
 
 ax.set_xlim(-radius*1.5, radius*1.5)
 ax.set_ylim(-radius, height + radius)
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $30$
Find the surface area of the solid figure shown. The radius is 6 cm.

Give your answer to the nearest two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 radius = 7
 height = 12
 
 fig, ax = plt.subplots(figsize=(6,10))
 
 theta = np.linspace(0, 2*np.pi, 100)
 x_top = radius * np.cos(theta)
 y_top = radius/2 * np.sin(theta) + height
 
 x_bottom = radius * np.cos(theta)
 y_bottom = radius/2 * np.sin(theta)
 
 ax.plot([radius, radius], [height, 0], color='k')
 ax.plot([-radius, -radius], [height, 0], color='k')
 
 ax.plot(x_top, y_top, color='k')
 ax.plot(x_bottom[50:], y_bottom[50:], color='k')
 
 theta_hidden = np.linspace(np.pi, 2*np.pi, 100)
 x_hidden = radius * np.cos(theta_hidden)
 y_hidden = radius/2 * np.sin(theta_hidden) + height
 ax.plot(x_hidden, y_hidden, color='k', alpha=0.3, linestyle='dashed')
 
 ax.plot([0, radius], [height, height], color='k')
 ax.text(radius/2, height+0.5, '6 cm', fontsize=12, style='italic', ha='center')
 
 ax.text(radius+1.5, height/2, '10 cm', fontsize=12, style='italic', ha='center')
 
 ax.set_xlim(-10, 12)
 ax.set_ylim(-6, 16)
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $603.19$
Find the surface area of the solid figure shown.

Round your answer to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 fig, ax = plt.subplots(figsize=(5,5))
 
 circle = plt.Circle((0, 0), 3, fill=False, linewidth=3, color='#19bfa7')
 ax.add_patch(circle)
 
 theta = np.linspace(0, 2*np.pi, 100)
 x = 3 * np.cos(theta)
 y = 1.5 * np.sin(theta)
 ax.plot(x, y, linestyle="--", color='#19bfa7')
 ax.plot(0, 0, 'o', color='#2c3e50', markersize=10)
 
 ax.plot([0, 3], [0, 0], linestyle='--', linewidth=3, color="blue")
 
 ax.text(1, 0.1, '11cm', fontsize=16)
 
 ax.set_aspect('equal')
 ax.axis('off')
 ax.set_xlim(-3.5, 3.5)
 ax.set_ylim(-3.5, 3.5) 
[/python]

Answer: $1520.53$
Find the surface area of the solid figure shown.

Round your answer to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 fig, ax = plt.subplots(figsize=(5,5))
 
 circle = plt.Circle((0, 0), 3, fill=False, linewidth=3, color='#2c3e50')
 ax.add_patch(circle)
 
 theta = np.linspace(0, 2*np.pi, 100)
 y = 3 * np.cos(theta)
 x = 1.1 * np.sin(theta)
 ax.plot(x, y, linestyle="--", color='#2c3e50')
 ax.plot(0, 0, 'o', color='#2c3e50', markersize=10)
 
 ax.plot([0, 0], [3, -3], color='#2c3e50', linestyle='-', linewidth=3)
 
 ax.text(0.2, 0.1, '9 cm', fontsize=16)
 
 ax.set_aspect('equal')
 ax.axis('off')
 ax.set_xlim(-3.5, 3.5)
 ax.set_ylim(-3.5, 3.5) 
[/python]

Answer: $254.47$
Find the surface area of the following solid figure.

Round your answer to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 # Set up the plot
 fig, ax = plt.subplots(figsize=(6,6))
 radius = 30
 
 # Draw the main circle (sphere)
 circle = plt.Circle((0, 0), radius, fill=False, color='black')
 ax.add_artist(circle)
 
 # Draw the dashed radius (equator perspective)
 theta = np.linspace(0, 2*np.pi, 200)
 x_ellipse = radius * np.cos(theta)
 y_ellipse = 0.4 * radius * np.sin(theta)   # Slightly "flatten" to suggest equator
 
 ax.plot(x_ellipse, y_ellipse, 'k--')
 
 # Draw the radius line
 ax.plot([0, radius], [0, 0], 'k')
 
 # Add the radius text
 plt.text(radius/2-5, 1, '56.17 $mm$', fontsize=14, fontstyle='italic')
 
 # Formatting
 ax.set_aspect('equal')
 ax.set_xlim(-radius*1.2, radius*1.2)
 ax.set_ylim(-radius*1.2, radius*1.2)
 ax.axis('off')
 
 plt.show() 
[/python]

Answer: $39647.77$
What is the area of the circular base of the solid figure?

Round your answer to three decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 fig, ax = plt.subplots(figsize=(6,4))
 
 radius = 7
 
 theta = np.linspace(np.pi, 2*np.pi, 100)
 x_semi = radius * np.cos(theta)
 y_semi = radius * np.sin(theta)
 ax.fill(x_semi, -radius-y_semi, color='olive', zorder=1)
 ax.plot(x_semi, -radius-y_semi, color='#22313F', linewidth=3)
 
 
 
 a = radius
 b = radius/3
 t = np.linspace(0, 2*np.pi, 100)
 x_ellipse = a * np.cos(t)
 y_ellipse = -radius + b * np.sin(t)
 ax.plot(x_ellipse, y_ellipse, color='#22313F', linewidth=2, linestyle='--')
 ax.fill_between(x_ellipse, y_ellipse, -radius, color='olive', alpha=0.7, zorder=2)
 
 ax.plot([0, 0], [0, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.plot([0, a], [-radius, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.text(0.3, -radius/2, '6', fontsize=16)
 
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $113.097$
Find the total surface area.

Round your answer to three decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 fig, ax = plt.subplots(figsize=(6,4))
 
 radius = 7
 
 theta = np.linspace(np.pi, 2*np.pi, 100)
 x_semi = radius * np.cos(theta)
 y_semi = radius * np.sin(theta)
 ax.fill(x_semi, -radius-y_semi, color='olive', zorder=1)
 ax.plot(x_semi, -radius-y_semi, color='#22313F', linewidth=3)
 
 
 
 a = radius
 b = radius/3
 t = np.linspace(0, 2*np.pi, 100)
 x_ellipse = a * np.cos(t)
 y_ellipse = -radius + b * np.sin(t)
 ax.plot(x_ellipse, y_ellipse, color='#22313F', linewidth=2, linestyle='--')
 ax.fill_between(x_ellipse, y_ellipse, -radius, color='olive', alpha=0.7, zorder=2)
 
 ax.plot([0, 0], [0, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.plot([0, a], [-radius, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.text(0.3, -radius/2, '8', fontsize=16)
 
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $603.186$
Find the surface area of the following solid figure.

Round your answer to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 fig, ax = plt.subplots(figsize=(6,4))
 
 radius = 7
 
 theta = np.linspace(np.pi, 2*np.pi, 100)
 x_semi = radius * np.cos(theta)
 y_semi = radius * np.sin(theta)
 ax.fill(x_semi, -radius-y_semi, color='olive', zorder=1)
 ax.plot(x_semi, -radius-y_semi, color='#22313F', linewidth=3)
 
 
 
 a = radius
 b = radius/3
 t = np.linspace(0, 2*np.pi, 100)
 x_ellipse = a * np.cos(t)
 y_ellipse = -radius + b * np.sin(t)
 ax.plot(x_ellipse, y_ellipse, color='#22313F', linewidth=2, linestyle='--')
 ax.fill_between(x_ellipse, y_ellipse, -radius, color='olive', alpha=0.7, zorder=2)
 
 ax.plot([0, 0], [0, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.plot([0, a], [-radius, -radius], color='#22313F', linestyle='--', linewidth=2)
 
 ax.text(-2, -radius/2, '$74.74cm$', fontsize=16)
 
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $52647.45$
One side of the left solid figure is 33. The height of middle solid figure is 11.

Find the surface area of the solid.

Round your answer to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 import matplotlib.patches as patches
 
 
 fig, ax = plt.subplots(figsize=(8,4))
 
 width, height = 15, 20
 
 # 梯形前底为14，上底10，高3，左偏移2，右偏移2
 # 前侧梯形
 A = np.array([0, 0])
 B = np.array([width, 0])
 D = A + np.array([0, height])
 C = B + np.array([0, height])
 
 # 棱柱厚度
 dx, dy = -5, 6
 dxy = np.array([dx, dy])
 # 后面四个点
 A1 = A + dxy
 B1 = B + dxy
 C1 = C + dxy
 D1 = D + dxy
 
 x0 = np.array([25, 0])
 A2 = A + x0
 B2 = B + x0
 C2 = C + x0
 D2 = D + x0
 
 A3, B3, C3, D3 = A1 + x0,  B1 + x0, C1 + x0, D1 + x0
 
 for X, Y in [(A, B), (B, C), (C, D), (D, A)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k')
 
 for X, Y in [(C1, D1), (D1, A1), (D, D1), (C, C1), (A, A1), (A2, A3)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k')
 
 for X, Y in [(A2, B2), (B2, C2), (C2, D2), (D2, A2)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k')
 
 for X, Y in [(C3, D3), (D3, A3), (D2, D3), (C2, C3)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k')
 
 for X, Y in [(A1, B1), (B1, C1), (A3, B3), (B3, C3), (B, B1), (B2, B3)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k--')
 
 # Big cylinder base
 main1 = patches.Arc(((B1[0] + B[0])/2, ((B1[1] + C1[1])/2 + (B[1] + C[1])/2)/2), 3, 13, theta1=0, theta2=360, color='black', linewidth=2, linestyle='--')
 #ax.plot([0, 0], [0, 0], 'ko')
 ax.add_patch(main1)
 
 main2 = patches.Arc(((A2[0] + A3[0])/2, ((A1[1] + D1[1])/2 + (A[1] + D[1])/2)/2), 3, 13, theta1=270, theta2=90, color='black', linewidth=2)
 main3 = patches.Arc(((A2[0] + A3[0])/2, ((A1[1] + D1[1])/2 + (A[1] + D[1])/2)/2), 3, 13, theta1=90, theta2=270, color='black', linewidth=2, linestyle='--')
 #ax.plot([0, 0], [0, 0], 'ko')
 ax.add_patch(main2)
 ax.add_patch(main3)
 
 ax.plot([(B1[0] + B[0])/2, (A2[0] + A3[0])/2], [((B1[1] + C1[1])/2 + (B[1] + C[1])/2)/2 + 6.5, ((B1[1] + C1[1])/2 + (B[1] + C[1])/2)/2 + 6.5], 'k')
 ax.plot([(B1[0] + B[0])/2, (A2[0] + A3[0])/2], [((B1[1] + C1[1])/2 + (B[1] + C[1])/2)/2 - 6.5, ((B1[1] + C1[1])/2 + (B[1] + C[1])/2)/2 - 6.5], 'k')
 
 
 ax.plot([B[0], A2[0]], [-2, -2], 'k')
 ax.plot([B[0], B[0]], [-1, -3], 'k')
 ax.plot([A2[0], A2[0]], [-1, -3], 'k')
 ax.plot([(A2[0] + A3[0])/2, (A2[0] + A3[0])/2], [((A1[1] + D1[1])/2 + (A[1] + D[1])/2)/2, ((A1[1] + D1[1])/2 + (A[1] + D[1])/2)/2+6.5], 'k')
 
 ax.text(B2[0] + 1, C[1]/2, r"$20$", fontsize=12, style='italic')
 ax.text((B2[0] + A2[0])/2, -2, r"$25$", fontsize=12, style='italic')
 
 ax.text((A2[0] + A3[0])/2-1.2, ((A1[1] + D1[1])/2 + (A[1] + D[1])/2)/2+0.5, r"$6$", fontsize=10, style='italic')
 
 ax.set_aspect('equal')
 ax.axis('off')
 plt.xlim(-8, 60)
 plt.ylim(-5, 30)
 plt.tight_layout()
 plt.show() 
[/python]

Answer: $8128.50$
Find the surface area of the composite figure shown. The radius is 4 cm.

Round your answer to two decimal places.

[python]
 import numpy as np
 import matplotlib.pyplot as plt
 
 radius = 4 
 height = 9 
 
 fig = plt.figure(figsize=(6, 12))
 ax = fig.add_subplot(111)
 
 theta = np.linspace(0, np.pi, 100)
 x_hemisphere = radius * np.cos(theta)
 y_hemisphere = -radius * np.sin(theta)
 
 
 x_cone = np.array([-radius, 0, radius])
 y_cone = np.array([0, height, 0])
 
 ax.plot(x_hemisphere, y_hemisphere, color='deepskyblue', linewidth=4)
 ax.fill_between(x_hemisphere, y_hemisphere, 0, color='deepskyblue', alpha=0.6)
 
 
 theta = np.linspace(0, 2*np.pi, 200)
 x_circle = radius * np.cos(theta)
 y_circle = radius/ 5 * np.sin(theta)
 ax.plot(x_circle, y_circle, color="deepskyblue", linewidth=4)
 ax.fill_between(x_circle, y_circle, 0, color="gray")
 ax.plot([-radius, 0], [0, height], color='gray')
 ax.plot([radius, 0], [0, height], color='gray')
 
 ax.plot([0, 0], [0, height], 'k--', lw=1)
 ax.text(0.1, height/1.7, r'$10cm$', fontsize=15)
 
 ax.plot([0, radius], [0, 0], 'black', linestyle='dashed')
 
 ax.plot([0.5, 0.5], [0, 0.5], color='black')
 ax.plot([0, 0.5], [0.5, 0.5], color='black')
 
 ax.axis('off')
 
 ax.set_aspect('equal')
 ax.set_xlim(-7, 7)
 ax.set_ylim(-6, 13) 
[/python]

Answer: $235.87$
The height of the bottom solid figure is 33.1 mm.

Hence find the total surface area of the shape, correct to two decimal places.

[python]
 import matplotlib.pyplot as plt
 import numpy as np
 
 # Parameters
 diameter = 9 
 radius = diameter / 2
 height = 18  
 
 fig, ax = plt.subplots(figsize=(4, 6))
 
 theta = np.linspace(np.pi, 2 * np.pi, 100)
 x = radius * np.cos(theta)
 y = radius * 0.25 * np.sin(theta) - height 
 
 ax.plot(x, y, color='teal', linewidth=2)
 
 top_y = 0
 top_ellipse = radius * np.cos(theta)
 top_ellipse_y = radius * 0.25 * np.sin(theta) + top_y
 
 ax.plot(top_ellipse, top_ellipse_y, color='teal', linewidth=2, alpha=1, solid_capstyle='round')
 
 theta = np.linspace(0, np.pi, 100)
 ax.plot(radius * np.cos(theta), 
         radius * 0.25 * np.sin(theta) - height, 
         '--', color='teal', alpha=0.5, linewidth=2) 
 
 ax.plot(radius * np.cos(theta), 
         radius * 0.25 * np.sin(theta), 
         '--', color='teal', alpha=0.5, linewidth=2) 
 
 ax.plot([radius, radius], [top_y, -height], color='teal', linewidth=2)
 ax.plot([-radius, -radius], [top_y, -height], color='teal', linewidth=2)
 
 theta2 = np.linspace(0, np.pi, 100)
 x2 = radius * np.cos(theta2)
 y2 = radius * np.sin(theta2)
 
 ax.plot(x2, y2, color='teal', linewidth=2)
 
 ax.annotate(
     '', xy=(0, -height-2), xytext=(radius, -height-2),
     arrowprops=dict(arrowstyle='<->', color='#43536D', linewidth=2)
 )
 ax.text(radius/2, -height-3, f"10.5 mm", ha='center', va='top', fontsize=14, color="#43536D")
 
 ax.plot([radius+1.2, radius+1.2], [-height, 0], color='#43536D', linewidth=2)
 ax.plot([radius+0.8, radius+1.6], [0, 0], color='#43536D', linewidth=2)
 ax.plot([radius+0.8, radius+1.6], [-height, -height], color='#43536D', linewidth=2)
 
 ax.set_aspect('equal')
 ax.axis('off') 
[/python]

Answer: $3222.80$
A solid figure has one side of length 14cm as shown.

If the size of \angle DFH is \theta °, find theta to two decimal places.

[python]
 import numpy as np
 import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d.art3d import Poly3DCollection
 
 length = 9 
 width = 4
 height = 4
 
 C = np.array([0, width, height])
 B = np.array([length, width, height])
 A = np.array([length, 0, height])
 D = np.array([0, 0, height])
 F = np.array([length, width, 0])
 E = np.array([length, 0, 0])
 H = np.array([0, 0, 0])
 G = np.array([0, width, 0])
 
 verts = [A, B, C, D, E, F, G, H]
 
 fig = plt.figure(figsize=(8,6))
 ax = fig.add_subplot(111, projection='3d')
 
 for point, name in zip(verts, ['A','B','C','D','E','F','G','H']):
     ax.scatter(*point, s=40)
     ax.text(*(point + np.array([0.2,0.2,0.2])), name, fontsize=12, color='k')
 
 edges = [
     (C, B), (B, A), (A, D), (D, C),
     (E, F), (E, H), (G, H), (G, F),
     (C, G), (B, F), (A, E), (D, H) 
 ]
 for edge in edges:
     ax.plot(*zip(*edge), color='k')
 
 ax.plot(*zip(*[D, F]), 'r--')
 ax.plot(*zip(*[H, F]), 'g--')
 ax.plot(*zip(*[E, F]), 'b--')
 
 arc_radius = 0.5
 angle = np.arctan(width/length)
 angle_values = np.linspace(0, angle, 30)
 arc_x = length - arc_radius * np.cos(angle_values)
 arc_y = width - arc_radius * np.sin(angle_values)
 arc_z = np.zeros_like(arc_x)
 ax.plot(arc_x, arc_y, arc_z, 'b')
 
 ax.text(length-0.3, width-1, 0, r'$\theta$', color='b', fontsize=16)
 
 ax.set_xlim([-.5, length+1])
 ax.set_ylim([-.5, width+1])
 ax.set_zlim([-.5, height+1])
 
 ax.text(0, width, height/2, '3 cm', color='k', fontsize=12)
 ax.text(-0.5, width/3, height+0.3, '3 cm', color='k', fontsize=12)
 ax.text(length/2, 1.5, -0.5, 'z cm', color='k', fontsize=12)
 
 ax.set_box_aspect([2,1,1])
 ax.axis('off')
 plt.tight_layout() 
[/python]

Answer: $11.83$
All edges of the following solid are 7 cm long.Find z, the size of \angle AGH, correct to 2 decimal places.

[python]
 import matplotlib.pyplot as plt
 
 fig, ax = plt.subplots(figsize=(4, 3))
 
 
 O = [0, 0]
 A = [-5.1, 4.1]
 B = [5.1, 4.1]
 C = [5.1, -4.1]
 D = [-5.1, -4.1]
 E = [2, 6]
 F = [12.2, 6]
 G = [12.2, -2.2]
 H = [2, -2.2]
 
 ax.plot([A[0], B[0]], [A[1], B[1]], color='black')
 ax.plot([B[0], C[0]], [B[1], C[1]], color='black')
 ax.plot([C[0], D[0]], [C[1], D[1]], color='black')
 ax.plot([D[0], A[0]], [D[1], A[1]], color='black')
 
 ax.plot([E[0], F[0]], [E[1], F[1]], color='black')
 ax.plot([F[0], G[0]], [F[1], G[1]], color='black')
 ax.plot([G[0], C[0]], [G[1], C[1]], color='black')
 
 ax.plot([A[0], E[0]], [A[1], E[1]], color='black')
 ax.plot([B[0], F[0]], [B[1], F[1]], color='black')
 
 for X, Y in [(H, E), (H, D), (H, G)]:
     ax.plot([X[0],Y[0]], [X[1],Y[1]], 'k')
 
 ax.text(A[0]-1, A[1], r"$D$", fontsize=12, style='italic')
 ax.text(B[0]-0.5, B[1]+0.5, r"$C$", fontsize=12, style='italic')
 ax.text(C[0], C[1]-1, r"$G$", fontsize=12, style='italic')
 ax.text(D[0], D[1]-1, r"$H$", fontsize=12, style='italic')
 ax.text(E[0], E[1]+0.5, r"$A$", fontsize=12, style='italic')
 ax.text(F[0], F[1]+0.5, r"$B$", fontsize=12, style='italic')
 ax.text(G[0], G[1]-1, r"$F$", fontsize=12, style='italic')
 ax.text(H[0]-1, H[1], r"$E$", fontsize=12, style='italic')
 
 ax.axis('off')
 plt.tight_layout()
 plt.show() 
[/python]

Answer: $54.74$
Find the length of AF, where $AB=2, BC=3, CD=6$.

[python]
 import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d.art3d import Poly3DCollection
 import numpy as np
 
 A = np.array([0, 0, 0])
 B = np.array([1, 0, 0])
 C = np.array([1, 1, 0])
 D = np.array([0, 1, 0])
 E = np.array([1, 1, 1.5])
 F = np.array([0, 1, 1.5])
 
 fig = plt.figure()
 ax = fig.add_subplot(111, projection='3d')
 
 verts = [A, B, C, D, E, F]
 
 edges = [
     [A, B], [B, C],
     [E, F], [A, E],
     [A, F], [B, E], [C, E]
 ]
 for edge in edges:
     ax.plot(*zip(*edge), color='black', linestyle='-', linewidth=1)
 
 edges = [[A,D], [C, D], [F, D]]
 for edge in edges:
     ax.plot(*zip(*edge), color='black', linestyle='--', linewidth=1)
 
 ax.plot(*zip(A, E), color='red', linewidth=2)
 
 labels = ['A', 'B', 'D', 'C', 'E', 'F']
 label_indices = [0, 1, 3, 2, 4, 5]
 for label, idx in zip(labels, label_indices):
     ax.text(*(verts[idx] + 0.05), label, fontsize=12)
 
 ax.set_box_aspect([1,1,1.5])
 ax.view_init(20, -30)
 ax.axis('off') 
[/python]

Answer: $7$
The solid is 3 cm thick. Calculate the volume of the solid, correct to one decimal places.

[python]

import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots(figsize=(4,4))

theta1 = 24
theta2 = 66
r = 9

angle = np.deg2rad(np.linspace(theta1, theta2, 200))
x_arc = r * np.cos(angle)
y_arc = r * np.sin(angle)

ax.plot(x_arc, y_arc, color="black")

ax.plot([0, x_arc[0]], [0, y_arc[0]], color="black")
ax.plot([0, x_arc[-1]], [0, y_arc[-1]], color="black")
ax.plot([0, 0], [0, -0.3], color="black")
ax.plot([x_arc[0], x_arc[0]], [y_arc[0], y_arc[0]-0.3], color="black")
ax.plot([0, x_arc[0]], [-0.3, y_arc[0]-0.3], color="black")


ax.text(1.2, 1.3, r"$42^\circ$", fontsize=16)

arc_mid = 0
x_label = (r+0.2)*np.cos(np.deg2rad(arc_mid))/2
y_label = (r+0.2)*np.sin(np.deg2rad(arc_mid)) +1
ax.text(x_label, y_label-0.4, "9", fontsize=16, ha='center')

ax.set_aspect('equal')
ax.set_xlim(-1.5, r+1)
ax.set_ylim(-1.5, r+2)
ax.axis('off')

plt.tight_layout()
plt.show()[/python]

Answer: $89.1$
Find the volume of the figure shown, correct to two decimal places. The height of both solid figures is 2 cm.

[python]
import matplotlib.pyplot as plt
import matplotlib.patches as patches

fig, ax = plt.subplots(figsize=(6,6))

main = patches.Arc((0, 0), 18, 4, theta1=180, theta2=360, color='black', linewidth=2)
ax.add_patch(main)

top_main = patches.Arc((0, 3), 18, 4, theta1=-204, theta2=24, color='black', linewidth=2)
ax.add_patch(top_main)

small = patches.Arc((0, 3), 8, 2, theta1=180, theta2=360, color='black', linewidth=2)
ax.add_patch(small)

ax.plot([-4, -4], [3, 7], color='black', linewidth=2)
ax.plot([4, 4], [3, 7], color='black', linewidth=2)


ax.plot([-9, -9], [0, 3], color='black', linewidth=2)
ax.plot([9, 9], [0, 3], color='black', linewidth=2)

top_small = patches.Ellipse((0, 7), 8, 2, fill=False, color='black', linewidth=2)
ax.add_patch(top_small)

ax.plot([0, 9], [0, 0], color='black')
ax.plot([0, 0], [0, 0], 'ko')
ax.text(4.5, 0.1, "$\\bf{9\\ cm}$", fontsize=14, style='italic')

ax.plot([0, 4], [7, 7], color='black')
ax.plot([0, 0], [7, 7], 'ko')
ax.text(2, 7.3, "$\\bf{4\\ cm}$", fontsize=14, style='italic')

ax.set_aspect('equal')
ax.set_xlim(-12, 15)
ax.set_ylim(-4, 12)
ax.axis('off')

plt.show()[/python]

Answer: $609.47$
The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places.

[python]
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(4, 3))


O = [0, 0]
A = [-5, 4]
B = [5, 4]
C = [5, -4]
D = [-5, -4]
E = [2, 10]
F = [12, 10]
G = [12, 2]
ax.plot([A[0], B[0]], [A[1], B[1]], color='black')
ax.plot([B[0], C[0]], [B[1], C[1]], color='black')
ax.text(B[0] + 0.5, 0, "$\\bf{8\\ cm}$", fontsize=11)
ax.plot([C[0], D[0]], [C[1], D[1]], color='black')
ax.plot([D[0], A[0]], [D[1], A[1]], color='black')

ax.plot([E[0], F[0]], [E[1], F[1]], color='black')
ax.plot([F[0], G[0]], [F[1], G[1]], color='black')
ax.plot([G[0], C[0]], [G[1], C[1]], color='black')
ax.text((C[0] + G[0]) / 2 + 0.5, (C[1] + G[1]) / 2 - 0.5, "$\\bf{14\\ cm}$", fontsize=11)

ax.plot([A[0], E[0]], [A[1], E[1]], color='black')
ax.plot([B[0], F[0]], [B[1], F[1]], color='black')


top_small = patches.Circle((0, 0), 2, fill=False, color='black', linewidth=2)
ax.plot([0, 2], [0, 0], color='black')
ax.add_patch(top_small)

ax.text(0 - 1.3, -A[1] - 1, "$\\bf{10\\ cm}$", fontsize=11)

ax.axis('off')
plt.tight_layout()
plt.show()[/python]

Answer: $944.07$
Find the total surface area of the solid with a side length equal to 6 cm.

[python]
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(4, 3))


O = [0, 0]
A = [-5.1, 4.1]
B = [5.1, 4.1]
C = [5.1, -4.1]
D = [-5.1, -4.1]
E = [2, 6]
F = [12.2, 6]
G = [12.2, -2.2]
ax.plot([A[0], B[0]], [A[1], B[1]], color='black')
ax.plot([B[0], C[0]], [B[1], C[1]], color='black')
ax.plot([C[0], D[0]], [C[1], D[1]], color='black')
ax.plot([D[0], A[0]], [D[1], A[1]], color='black')

ax.plot([E[0], F[0]], [E[1], F[1]], color='black')
ax.plot([F[0], G[0]], [F[1], G[1]], color='black')
ax.plot([G[0], C[0]], [G[1], C[1]], color='black')

ax.plot([A[0], E[0]], [A[1], E[1]], color='black')
ax.plot([B[0], F[0]], [B[1], F[1]], color='black')

ax.plot([0, 0], [-3.8, -4.4], color='black')

ax.plot([0, 0], [3.8, 4.4], color='black')
ax.plot([0, 0], [-3.8, -4.4], color='black')
ax.plot([7.1, 7.1], [5.7, 6.3], color='black')

ax.plot([-4.8, -5.4], [0, 0], color='black')
ax.plot([11.9, 12.4], [2, 2], color='black')
ax.plot([4.8, 5.4], [0, 0], color='black')
ax.plot([-1.6, -1.3], [5.40, 4.80], color='black')
ax.plot([8.6, 8.8], [-2.8, -3.4], color='black')
ax.text(0 - 1.3, -A[1] - 1, "$\\bf{6\\ cm}$", fontsize=11)

ax.axis('off')
plt.tight_layout()
plt.show()[/python]

Answer: $216$
Find the surface area of the solid figure with length equal to 12 m.

[python]
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(4, 3))


O = [0, 0]
A = [-5.1, 3.1]
B = [5.1, 3.1]
C = [5.1, -3.1]
D = [-5.1, -3.1]
E = [5, 10]
F = [15.2, 10]
G = [15.2, 3.8]
ax.plot([A[0], B[0]], [A[1], B[1]], color='black')
ax.plot([B[0], C[0]], [B[1], C[1]], color='black')
ax.plot([C[0], D[0]], [C[1], D[1]], color='black')
ax.plot([D[0], A[0]], [D[1], A[1]], color='black')

ax.plot([E[0], F[0]], [E[1], F[1]], color='black')
ax.plot([F[0], G[0]], [F[1], G[1]], color='black')
ax.plot([G[0], C[0]], [G[1], C[1]], color='black')

ax.plot([A[0], E[0]], [A[1], E[1]], color='black')
ax.plot([B[0], F[0]], [B[1], F[1]], color='black')

ax.text(0 - 1.3, -A[1] - 1, "$\\bf{6\\ m}$", fontsize=11)
ax.text(A[0] - 4, 0, "$\\bf{4\\ m}$", fontsize=11)


ax.axis('off')
plt.tight_layout()
plt.show()[/python]

Answer: $288$