Chapter 12.2, Problem 4CYP

To determine

To calculate : To find diameter of a base of cylinder.

Answer to Problem 4CYP

The required diameter of a base of cylinder is $16\text{cm}$ .

Explanation of Solution

Given information : Surface area is $464\pi {\text{cm}}^2$ and height is $21\text{cm}$ .

Formula used : The surface area of cylinder is

  $\begin{array}{l}L=2\pi rh\\ S=L+2\pi r^2\end{array}$

Where, L is lateral area.

Calculation : The surface area of cylinder,

  $\begin{array}{l}464\pi =2\pi r\left(21+r\right)\\ 232=r\left(21+r\right)\\ r^2+21r-232=0\end{array}$

Simplify further,

  $\begin{array}{l}\left(r+29\right)\left(r-8\right)=0\\ r=-29\text{or}r=8\end{array}$

Negative value is not possible,

Therefore, the required diameter is $2\cdot 8=16\text{cm}$ .