Question

If the radius of a sphere increases from $4\text{cm}$ to $7\text{cm}$, then what is the difference between the volume of both the spheres ?

• A. $\frac{1327}{3}\pi$
• B. $\frac{1071}{3}\pi$
• C. $\frac{1583}{3}\pi$
• D. None of the above.

Answer 1

The correct option is B $\frac{1071}{3}\pi$

The figure as per the given data can be drawn as follows:


The formula to calculate the volume of sphere is given as $V=\frac{4}{3}\pi r^3$.

Let the original sphere be the sphere with radius $4\text{cm}$, therefore the volume of original sphere will be obtained as,

$\begin{array}{cc}\text{Volume of original sphere}& =\frac{4}{3}\pi \left(4^3\right)\\ & =\frac{256}{3}\pi \end{array}$

The radius of new sphere is $7\text{cm}$, therefore its volume is obtained as,

$\begin{array}{cc}\text{Volume of new sphere}& =\frac{4}{3}\pi \left(7^3\right)\\ & =\frac{1327}{3}\pi \end{array}$

Therefore, the difference between the volume of new and original sphere is,

$\begin{array}{cc}\text{Difference}& =\text{Volume of new sphere}-\text{Volume of original sphere}\\ & =\frac{1327}{3}\pi -\frac{256}{3}\pi \\ & =\frac{1071}{3}\pi \end{array}$