Chapter E, Problem 12.7EX

To determine

To find the height of the cylinder.

Answer to Problem 12.7EX

Option (c)

Explanation of Solution

Given information: The volume of cone and the radius of the cylinder are same. The radius and height of the cone is 5 and 12. Also, the radius of the cylinder are 10.

Concept used:

  $\begin{array}{l}\text{Volume}\text{of}\text{the}\text{cone}=\frac{1}{3}\pi r^{2}h\\ \text{Volume}\text{of}\text{the}\text{cylinder}=\pi r^{2}h\end{array}$

Let $r_1\text{and}{h}_1$ be the radius and height of the cone and Let $r_2\text{and}{h}_2$ be the radius and height of the cylinder.

According to the situation,

Volume of the Cone = Volume of the Cylinder

  $\begin{array}{l}\frac{1}{3}\pi r_1{}^2{h}_1=\pi r_2{}^2{h}_2\\ 25\times 12=100\times h_2\\ \Rightarrow h_2=3\end{array}$

Hence, the height of the cylinder is 3 units.