Chapter 8.3, Problem 49E

a.

To determine

To find : the plumb bob’s volume.

Answer to Problem 49E

The plumb bob’s volume is $\frac{36\pi }{5}$ .

Explanation of Solution

Given information : A brass plumb bob that will weigh in the neighbourhood of $190g$

the solid of revolution shown here:

  

Calculation :

The given shape about x -axis.

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{6}{\int }}\pi ·{\left(\frac{x}{12}\sqrt{36-x^2}\right)}^2}\\ \Rightarrow \frac{36\pi }{5}\end{array}$

b.

To determine

To find: How much the plumb bob weigh to the nearest gram.

Answer to Problem 49E

The plumb bob weigh is $192grams$ .

Explanation of Solution

Given information : A brass plumb bob that will weigh in the neighbourhood of $190g$ . If you specify a brass that weighs is $8.5\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.$

the solid of revolution shown here:

  

Calculation :

  $\begin{array}{l}\frac{36\pi }{5}\times 8.5\\ \Rightarrow 192.26grams\\ \approx 192grams\end{array}$