how many small pancakes will grandma's recipe make?

grandma has an old family recipe for blueberry pancakes.she can make 8 pancakes that are each 10 inches in diameter. grandma decided that the pancakes were way too large for her grandchildren and decided to make pancakes that were only 2 inches in diameter.how many small pancakes will grandma's recipe make?

the scale factor is 1/5.
the ratio of the areas is 1/25.
she can make 25 times as many pancakes.
(25)(8) = 200.
 
good sat question.

earlier grandma able make 8 pancakes of 10 inches.
each pancake's area  : pi * radius^2 pi * 5^2 = pi * 25.
 
so 8 pancake area 8*pi*25= 200 * pinow that she's making smaller pancakes of diameter 2(radius=1),
the area of each pancake
pi*1^2.= pi * 1.200* pi /pi * 1= 200
 
so she can make 200 pancake

hi young
 
the area of each large pancake is    pi*(d/2)2  where d is the diameter
 
for the larger pancakes, d=10 inch. then, each large pancake has an area of: 
 
  pi*(10/2)2  =  25*pi   (a)
 
because each small pancake has a diameter d=2 inch, the area of each small pancake is:
 
  pi*(2/2)2  =    pi         (b)
 
if you compare the areas (a) and (b), is concluded that each large pancake contains 25 small pancakes.
 
because, we have a total of 8 large pancakes, the total number of small pancakes is given by:  8*25 = 200
 
response: a total of 200 small pancakes
 
 
 

d1 = 10 inches
 
d2 = 2 inches
 
a1 = π(d1/2)2 = area of a 10 inch pancake
 
a2 = π(d2/2)2 = area of a 2 inch pancake
 
she can make pancakes whose total area is 8a1.  then the number of 2 inch pancakes she can make is just 8a1/a2.
 
8a1/a2 = 8 π(d1/2)2 / [π(d2/2)]2 = 8(d1/d2)2 = 8(10/2)2 = 8*25 = 200
 
she can make 200 of the 2-inch pancakes.
 

8 pancakes with a diameter of 10 inches;  radius = 5 inches
 
assuming the pancakes are circular, then 
 
area = ( 3.14 ) r2  ;   r is the radius = 5
 
8 ( area of one pancake ) = 8 (3.14) (5)2
 
total area of 8 pancakes   = 628 in.2 
 
looking at the smaller pancakes; diameter = 2 ; radius = 1
 
x = number of smaller pancakes that can be made,
      these would have the same total area as the larger cakes
 
             x (3.14 ) (1)2  = total area of pancakes with radius = 1
 
                         3.14x = 628
 
                                x = 200
 
you could make 200 pancakes of diameter = 2