Question

The surface area of a plastic ball is 196 pi. A sponge ball has a radius twice that of the plastic ball. What is the surface area of the sponge ball?

A. 9,604 pi
B. 993 pi
C. 784 pi
D. 546 pi
Explain your answer and please show all work.

Answer 1

Option C.
`784\pi\ units^(2)`

Explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area of the sponge ball

y----> surface area of a plastic ball

`z^(2)=(x)/(y)`

we have

`z=2`

`y=196\pi\ units^(2)`

substitute and solve for x

`2^(2)=(x)/(196\pi)`

`x=4*(196\pi)=784\pi\ units^(2)`