Mark M. answered • 08/12/16

Mathematics Teacher - NCLB Highly Qualified

Young K.

asked • 08/11/16Grandma 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?

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?

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Mark M. answered • 08/12/16

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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.

Namita S. answered • 08/12/16

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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),

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

Nicolas M. answered • 08/12/16

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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

Arturo O. answered • 08/12/16

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d_{1} = 10 inches

d_{2} = 2 inches

A_{1} = π(d_{1}/2)^{2} = area of a 10 inch pancake

A_{2} = π(d_{2}/2)^{2} = area of a 2 inch pancake

She can make pancakes whose total area is 8A_{1}. Then the number of 2 inch pancakes she can make is just 8A_{1}/A_{2}.

8A_{1}/A_{2} = 8 π(d_{1}/2)^{2} / [π(d_{2}/2)]^{2} = 8(d_{1}/d_{2})^{2} = 8(10/2)^{2} = 8*25 = 200

Neal D. answered • 08/12/16

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8 pancakes with a diameter of 10 inches; radius = 5 inches

Assuming the pancakes are circular, then

Area = ( 3.14 ) r^{2} ; 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

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