Question

If the radius of the sphere is increased by 100% the volume of the corresponding sphere is increased by

Answer 1

Let the radius of the sphere be r. 

⇒ Volume = 2πr³/3

Now, new radius = r + 100% of r = 2r 

⇒ New volume = 4π(2r)³/3 = 32πr³/3

Increase in volume = 32πr³/3 - 4πr³/3 = 28πr³/3

∴ Percentage increase = \(\frac{28 \pi r^3/3}{4\pi r^3 /3} \times 100\)

⇒ 700%

∴ The volume of the corresponding sphere is increased by 700%.

Answer 2

Initial Volume (V) of sphere = \(\frac{4}{3} \pi r^3\)

If the radius of a sphere increases by 100%, it means the radius is doubled.

New volume of sphere is V₁.

Now V₁ = \(\frac{4}{3} \pi (2r)^3\)

So, volume will be 8 times the original volume.

%change in volume = \((\frac{8v-v}{v}) \times 100\) = 700%