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german
3 years ago
9

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 are

a 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.
Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0

Answer:

Option C. 784\pi\ units^{2}

Step-by-step 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}=\frac{x}{y}

we have

z=2

y=196\pi\ units^{2}

substitute and solve for x

2^{2}=\frac{x}{196\pi}

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

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