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A small sphere has a radius of 5 cm. A larger sphere is created by uniformly expanding the smaller sphere. The radius of the larger sphere is 15 cm. H
Question

A small sphere has a radius of 5 cm. A larger sphere is created by uniformly expanding the smaller sphere. The radius of the larger sphere is 15 cm. How many times greater is the surface area of the larger sphere compared to the smaller sphere?

A.

15 times

B.

9 times

C.

3 times

D.

6 times

Correct option is B

Given:
Radius of the smaller sphere(r1) (r_1)​ = 5 cm
Radius of the larger sphere(r2) (r_2)​ = 15 cm
Formula Used:
Surface Area of a sphere =4πr2= 4\pi r^2​​
Ratio of Surface Areas = (r2r1)2 (\frac{r_2}{r_1})^2​​
Solution:
Ratio of radii = 155\frac{15}{5}​ = 3
Ratio of Surface Areas = 323^2 ​= 9
The surface area of the larger sphere is 9 times greater.
Final Answer
So the correct answer is (b)

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