Question

The volume of the cone with circular base is \[216\pi {\text{ cu}}{\text{.cm}}\], If the base radius is 9 cm, then find the height (in cm) of the cone.

Answer 1

Hint: The volume of the cone with circular base having radius \[r\]and height \[h\]is given by the formula \[V = \dfrac{1}{3}\pi {r^2}h\]. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:

Given volume of the cone \[V = 216\pi {\text{ cu}}{\text{.cm}}\]

Radius of the cone \[r = 9{\text{ cm}}\]

Let \[h\] be the height of the given cone.

We know that the volume of the cone with a circular base is given by \[V = \dfrac{1}{3}\pi {r^2}h\].

By the above data, we have

\[ \Rightarrow \dfrac{1}{3}\pi {r^2}h = 216\pi \]

Cancelling \[\pi \]on both sides and substituting the value \[r = 9{\text{ cm}}\], we get

\[

   \Rightarrow \dfrac{1}{3}{\left( 9 \right)^2}h = 216 \\

   \Rightarrow \dfrac{{9 \times 9}}{3}h = 216 \\

   \Rightarrow 27h = 216 \\

   \Rightarrow h = \dfrac{{216}}{{27}} \\

  \therefore h = 8{\text{ cm}} \\

\]

Thus, the volume of the cone with a circular base is 8 cm.

Note: In the question the volume of the cone with circular base is given in cu.cm and the radius of it is given in cm. So, to find the height in centimetres (cm) we don’t need to do any conversions into the dimensions of the cube.