How many small pancakes will Grandma's recipe make?

Question

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?

Answer 1

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.

Answer 2

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 * pi

Now 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

Answer 3

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

 

 

 

Answer 4

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.

 

Answer 5

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