LiAuto-DSR/GeoGramBench huggingface dataset:
Two similar solids as shown in the figure, the larger solid has volumes of 5760\mathrm{cm}^3.


Find the fully simplified ratio of the volume of the larger solid to the volume of the smaller solid.

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

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

r = 5
R = 10
H, h = 15, 10
OA = [0, 0]
OA1 = [0, H]
OB = [15, 0]
OB1 = [15, h]
mainA1 = patches.Arc((0, 0), R, r, theta1=0, theta2=180, color='black', linewidth=2, linestyle='--')
mainA2 = patches.Arc((0, 0), R, r, theta1=180, theta2=360, color='black', linewidth=2)
mainA3 = patches.Arc((0, H), R, r, theta1=0, theta2=360, color='black', linewidth=2)
mainB1 = patches.Arc((15, 0), r, 3, theta1=0, theta2=180, color='black', linewidth=2, linestyle="--")
mainB2 = patches.Arc((15, 0), r, 3, theta1=180, theta2=360, color='black', linewidth=2)
mainB3 = patches.Arc((15, h), r, 3, theta1=0, theta2=360, color='black', linewidth=2)
ax.add_patch(mainA1)
ax.add_patch(mainA2)
ax.add_patch(mainA3)
ax.add_patch(mainB1)
ax.add_patch(mainB2)
ax.add_patch(mainB3)
ax.plot([-R/2, -R/2], [0, H], color='black')
ax.plot([R/2, R/2], [0, H], color='black')

ax.plot([15-r/2, 15-r/2], [0, h], color='black')
ax.plot([15+r/2, 15+r/2], [0, h], color='black')


ax.text(12, -4, r"$Volume\,= \,90\,cm^3$", fontsize=12, style='italic')
ax.text(R/2+1, H/2, r"$c\,\,cm$", fontsize=12, style='italic')
ax.text(15+r/2+1, h/2, r"$20\,\,cm$", fontsize=12, style='italic')


ax.set_aspect('equal')
ax.set_xlim(-8, 20)
ax.set_ylim(-6, 20)
ax.axis('off')

plt.show()[/python]

Answer: $100$