Chapter 12.6, Problem 2CYU

To determine

The surface area and lateral surface area of the given cylinder is to be estimated.

  

Answer to Problem 2CYU

The surface area and lateral surface area of the given cylinder is $400f{t}^2$ and $47.12f{t}^2$ respectively.

Explanation of Solution

Given:

  $\begin{array}{l}r=7\frac{1}{2}=\frac{15}{2}ft\\ h=5ft\end{array}$

Concept Used:

The surface area of cylinderis given by the following expression:

  $A=2\pi rh+2\pi r^2$

The lateral surface area of cylinder is given by the following expression:

  $LSA=2\pi rh$

Where,

Radius of cylinder: $r$

Height of cylinder: $h$

Calculation:

The surface area of cylinder:

  $A=2\pi rh+2\pi r^2$

Put the given data:

  $\begin{array}{l}A=2\pi rh+2\pi r^2\\ A=2\pi \left(\frac{15}{2}\right)5+2\pi {\left(\frac{15}{2}\right)}^2\\ A=47.12+353.43\\ A=400f{t}^2\end{array}$

The lateral surface area of cylinder:

  $LSA=2\pi rh$

Put the given data:

  $\begin{array}{l}LSA=2\pi rh\\ LSA=2\pi \left(\frac{15}{2}\right)5\\ LSA=47.12f{t}^2\end{array}$

Conclusion:

Hence,

The surface area of cylinder is $A=400f{t}^2$

The lateral surface area of cylinder is $LSA=47.12f{t}^2$