Chapter 12.6, Problem 29PPS

To determine

Calculate the surface area and volume of the solid.

Answer to Problem 29PPS

The surface area and the volume are $276.3i{n}^2$ & $385i{n}^3$ .

Explanation of Solution

Given:

It is given in the question that the solid is given below:

  

Concept Used:

In this, use the concept surface area of the solid is $S=\pi r^2+2\pi rh+2\pi r^2$ and the volume of the solid will be $V=\pi r^{2}h+\frac{2}{3}\pi r^3$ .

Calculation:

Here, $r=4in,h=5in$

  $\begin{array}{l}S=\pi r^2+2\pi rh+2\pi r^2\\ S=2\pi rh+3\pi r^2\\ $ S=2\pi (4)(5)+3\pi {(4)}^2$S=40\pi +48\pi \\ S=88\pi \\ S=88\times 3.14=276.3i{n}^2\end{array}$

Now, volume of the solid,

  $\begin{array}{l}V=\pi r^{2}h+\frac{2}{3}\pi r^3\\ $ V=\pi {(4)}^2(5)+\frac{2}{3}\pi {(4)}^3$V=80\pi +42.6\pi \\ V=122.6\pi \\ V=385i{n}^3\end{array}$

Conclusion:

The surface area and the volume are $276.3i{n}^2$ & $385i{n}^3$ .