Chapter 12.6, Problem 30PPS

To determine

Calculate the surface area and volume of the solid.

Answer to Problem 30PPS

The surface area and the volume are $798.5c{m}^2$ & $1038.4c{m}^3$ .

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 $S=a^2-\pi r^2+\frac{1}{2}4\pi r^2$ + B + Ph and the volume of the solid will be $V=Bh-\frac{2}{3}\pi r^3$ .

Calculation:

Here, $r=\frac{10}{2}=5cm,h=13cm$

  $\begin{array}{l}$ S={10}^2-\pi {(5)}^2+\frac{1}{2}4\pi {(5)}^2+{10}^2+10\cdot 13\cdot 4$S=100-25\pi +50\pi +100+520\\ S=100+25\pi +620\\ S=720+78.5\\ S=798.5c{m}^2\end{array}$

Now, volume of the solid,

  $\begin{array}{l}V=Bh-\frac{2}{3}\pi r^3\\ $ V={10}^2(13)-\frac{2}{3}\pi {(5)}^3$V=1300-\frac{2}{3}\pi \times 125\\ V=1300-261.6\\ V=1038.4c{m}^3\end{array}$

Conclusion:

The surface area and the volume are $798.5c{m}^2$ & $1038.4c{m}^3$ .