a proportion problem?

Question

a certain recipe makes enough batter for exactly 8 circular pancakes that are each 10 inches in diameter. How many curcular pancakes, each 5 inches in diameter and of the same thickness as the 10 inch pancakes, should the recipe make?
well, the answer is 32, how come?

Answer 1

You're working with volume here...

The volume of a pancake in this situation is V=(pi)(r^2)(h) where h is the thickness and r is the radius (or 1/2 the diameter).

So for the 8 pancakes of 10" diameter...

Volume of 1 pancake = (pi)(5^2)(h) = 25(pi)(h)

So the amount of batter is 8(25)(pi)(h).

For the new 5" diameter pancakes (r = 5/2), the volume of 1 pancake = (pi)[(5/2)^2](h) = (25/4)(pi)(h). x is the number of pancakes we get, so the total batter is
x(25/4)(pi)h

Set those equal to each other because the total amount of batter doesn't change:

8(25)(pi)(h) = x(25/4)(pi)(h)
400 (pi)(h) = x(25/4)(pi)(h)
400 = 25x/4
1600 = 25x
32 = x

Answer 2

Area of 10" diameter pancakes = pi x r² = pi x 5² = 25pi
Area of 5" diameter pancakes = pi x 2.5² = 6.25pi
Now 6.25pi / 25pi = 1/4
Area of 5" diameter is 1/4 area of 10" diameter and will therefore be able to make 4x as much with the 5" diameter.
Hence answer of 4 x 8 = 32

Answer 3

Since thickness is same for 5" and 10 " than we have to calculate area and eualize the equations

Area of 10" x 8 nos = Area of 5" x n ( n = numbers of 5")

n = (PI/4 * 10^2 * 8)/ (PI/4 * 5^2 )

n = 100*8/25 = 32 numbers

Answer number of 5" = 32 numbers.
is it right?

Answer 4

Area of 1 10 inches pancake
=3.14x5x5
=78.5 sq inches

Area of 8 10 inches pancake
=78.5x8
=628 sq inches

Area of 1 5 inches pancake
=3.14x2.5x2.5
=19.625 sq inches

Use Total Area of 8 10 inches pancake / 5 inches pancake
=628/19.625
=32 nos

Answer 5

u can try it dis way.
Area of 1 10-in pancake = 3.14 x 5 x 5 = 78.5

Area of 8 10-in pancake = 78.5 x 8 = 628

number of pancakes = total area divide by area of 1 pancake ?

628/(3.14 x 2.5 x 2.5) = 32.... (2.5 being radius of smaller pancake

Answer 6

here number of pancakes are INVERSLY PROPORTIONAL the area of pancakes
BECAUSE IF AREA IS MORE THEN MORE TIME WILL REQUIRE
let N is the number of panckes
and A is area
therefor N is directly proportioanl to A

Let k is constant
so, 8=k/(10)^2
SO, K=800

Now, in second cases N=K/ 5^2
SO, N= 800/25
=32

Answer 7

n2 A2 = n1 A1

n2/n1 = A1/A2 = (R1/R2) ^2 = (10/5) ^2 = 4

n2 = 8x4 = 32.