What is the increase of surface area and volume of this sphere?

Question

A sphere with $r$ is doubling and its radius is being $2r$.

• What is the increase of surface area $\pi r^2$?

• What is the increase of its volume $\pi r^3$?

I know that

$$A = 4\pi r^2$$

And for volume

$$V = \frac{4}{3} \pi r^3$$

I'm getting wrong when I try to calculate.

Answer 1

Starting area of sphere is $A_1= 4\pi r^2.$ After doubling the radius, the new area is $A_2= 4\pi \,(2r)^2=16\pi r^2=4 \times A_1.$ So the new area is $4$ times the old area.

This will solve your doubt. Just see it and same can be done for volume.

Answer 2

I think you meant a sphere. For your question:
If radius of sphere is $7cm$ then it's area is $4\pi r^2 = 616$
Calculating with new radius we get answer as $2464$ which is $4$ times of previous one hence if radius is doubled then it's total surface area becomes $4$ times actual one
Similarly, in the case of volume it becomes $8$ times as original.