Question

If the radius of a sphere is increased by 20%,by what percent does its volume increases?​

Answer 1

volume is increased by 72.8%

Step-by-step explanation:

let the radius = r

then volume of sphere = $\frac{4}{3}\pi r^3$

when the radius is increased by 20%

the new radius = $r+\frac{20}{100}r = 1.2 r$

new volume is

$\frac{4}{3}\pi (1.2r)^3$

$= 1.728\times \frac{4}{3}\pi (r)^3$

% increase in the volume

$(1.728\times \frac{4}{3}\pi (r)^3- \frac{4}{3}\pi (r)^3)\times 100%\\\\0.728\times 100$

= 0.728 × 100

= 72.8 %

hence , volume is increased by 72.8%

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