Chapter 12, Problem 22RP

a.

To determine

Find the volume of the surface of rotation generated by rotating the figure about dashed line.

Answer to Problem 22RP

  $116cubicunit$

Explanation of Solution

Given information:

Given figure,

  

Calculation:

  $\begin{array}{l}hypotenuse=8\\ \sin 30°=\frac{p}{h}\\ p=h\times \sin 30°\\ p=8\times 0.5=4\\ base=\sqrt{8^2-4^2}\\ =\sqrt{64-16}\\ =4\sqrt{3}\\ V=\frac{1}{3}\pi h^{2}b\\ =\frac{1}{3}\pi \times 4\sqrt{3}\times 4^2\\ V=116cuunit\end{array}$

Hence, $V=116cuunit$

b.

To determine

Find the volume of the surface of rotation generated by rotating the figure about dashed line.

Answer to Problem 22RP

  $110cubicunit$

Explanation of Solution

Given information:

Given figure,

  

Calculation:

  $\begin{array}{l}V=\pi 4^2\times 5-\pi 3^2\times 5\\ =80\pi -45\pi \\ V=110cubicunit\end{array}$

Hence, $V=110cubicunit$