Question

If a sphere’s radius is quadrupled, what is the corresponding change in surface area? A. The surface area is quadrupled. B. The surface area is multiplied by 8. C. The surface area is multiplied by 16. D. The surface area is doubled.

Answer 1

Answer:

Option B. The surface area is multiplied by 16.

Step-by-step explanation:

Since surface are of a sphere is A = 4πr²

Now we quadruple the radius of this sphere then surface area becomes as

A' = 4π(4r)² = 4π(16r²) = 64πr²

If we find the ratio of these spheres

A/A' = 4πr²/64πr² = 1/16

A' = 16A

That means area of the new sphere gets multiplied by 16.

Therefore option C. is the answer.

Answer 2

$A=4\pi r^2$

Quadrupling the radius gives an area of

$A=4\pi(4r)^2=4^2\times4\pi r^2$

which is 16 times the original area.