Chapter 8.2, Problem 43PPE

a.

To determine

To write: The formula for the volume of the cube in terms of s

Answer to Problem 43PPE

  $V=64s^3$

Explanation of Solution

Given:

  

Calculation:

The formula for the volume of the general cube is:

  $\begin{array}{l}V={\left(side\right)}^3\\ V={\left(4s\right)}^3\\ \boxed{V=64s^3}\end{array}$

b.

To determine

To write: The formula for the volume of the cylinder in terms of s

Answer to Problem 43PPE

  $V=48\pi s^2$

Explanation of Solution

Given:

  

Calculation:

The formula for the volume of the general cylinder is:

  $\begin{array}{l}V=\pi r^{2}h\\ V=\pi s^2\left(48\right)\\ \boxed{V=48\pi s^2}\end{array}$

c.

To determine

To write: The formula for the volume left after the cylinder has been removed

Answer to Problem 43PPE

  $V=64s^3-48\pi s^2$

Explanation of Solution

Given:

  

Calculation:

The formula for the Volume left after the cylinder has been removed is:

  $\begin{array}{l}V=AreaofCube-AreaofCylinder\\ \boxed{V=64s^3-48\pi s^2}\end{array}$

d.

To determine

To find: factor of the formula in part c

Answer to Problem 43PPE

  $V=16s^2\left(4s-3\pi \right)$

Explanation of Solution

Given:

  

Calculation:

Factor of part c

  $\begin{array}{l}V=64s^3-48\pi s^2\\ \boxed{V=16s^2\left(4s-3\pi \right)}\end{array}$

e.

To determine

To find: The volume left after the cylinder has been removed when $s=15$ and $\pi =3.14$

Answer to Problem 43PPE

  $V=182.08i{n}^3$

Explanation of Solution

Given:

  

Calculation:

The volume left after the cylinder has been removed when $s=15$ and $\pi =3.14$ is

  $\begin{array}{l}V=16s^2\left(4s-3\pi \right)\\ V=16{\left(15\right)}^2\left[4\left(15\right)-3\left(3.14\right)\right]\\ V=16\left(225\right)\left[60-9.42\right]\\ V=\left(3600\right)\left(50.58\right)\\ \boxed{V=182.08i{n}^3}\end{array}$