Chapter E, Problem 12.6EX

To determine

To find the volume of the sphere.

Answer to Problem 12.6EX

Option (b)

Explanation of Solution

Given information: The area of the sphere is $16\pi$ .

Concept used:

Two cones are said to be similar, if their volumes are in the proportion as,

  $\begin{array}{l}\text{Volume}\text{of}\text{the}\text{sphere}=\frac{4}{3}\times \pi \times r^3\\ \text{Surface area}\text{of}\text{the}\text{sphere}=4\times \pi \times r^2\end{array}$

  $\begin{array}{l}\text{Surface area}\text{of}\text{the}\text{sphere}=4\times \pi \times r^2=16\pi \\ \Rightarrow r=2\end{array}$

  $\begin{array}{l}\text{Volume}\text{of}\text{the}\text{sphere}=\frac{4}{3}\times \pi \times r^3=\frac{32\pi }{3}\\ \end{array}$

Hence, the volume of the sphere is $\frac{32\pi }{3}$ cubic units.