Question

If the radius of the sphere is increased by $100\%$, the volume of the corresponding sphere is increased by-

• A. $200\%$
• B. $500\%$
• C. $700\%$
• D. $800\%$

Answer 1

The correct option is C $700\%$

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 $V_1$.
Now $V_1=\frac{4}{3}\pi (2r{)}^3$
$V_1=8V$
So, volume will be $8$ times the original volume.
$\%$ change in volume $=\left(\frac{8V-V}{V}\right)\times 100=700$ $\%$
So, option C is correct.