Chapter 13, Problem 5STP

To determine

The correct option which shows the total surface area of cylinder who has the height and diameter of $5.4in,3.8in$ respectively.

A. $87.1i{n}^2$

B. $73.3i{n}^2$

C. $61.2i{n}^2$

D. $55.4i{n}^2$

Answer to Problem 5STP

The correct option is A. Total surface area of cylinder is $87.1i{n}^2$ .

Explanation of Solution

Given:

  $\begin{array}{l}h=5.4in\\ d=3.8in\end{array}$

Concept Used:

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

  $SA=2\pi r\left(h+r\right)$

Where,

The heightof cylinder: $h$

Radius of cylinder: $r$

Calculation:

The total surface area of cylinder is calculated as:

  $SA=2\pi r\left(h+r\right)$

Put the given data in above eq.

  $\begin{array}{l}SA=2\pi r\left(h+r\right)\\ SA=2\pi \left(\frac{d}{2}\right)\left(h+\frac{d}{2}\right)\\ SA=2\pi \left(\frac{3.8}{2}\right)\left(5.4+\frac{3.8}{2}\right)\\ SA=2\pi \left(1.9\right)\left(5.4+1.9\right)\\ SA=87.1i{n}^2\end{array}$

Conclusion:

Hence,correct option is A.