Chapter 12.6, Problem 4PSA

a.

To determine

To find: The volume of the cylinder with height 8 and diameter 14.

Answer to Problem 4PSA

The volume of the cylinder is 1232.

Explanation of Solution

Given Information:

Diameter of a cylinder $\left(d\right)=14$

Height of a cylinder $\left(h\right)=8$

Formula used:

Volume of a cylinder $\left(V\right)=\pi r^{2}h$

  $r\text{and}h$ are the radius and height of a cylinder

Calculation:

The diameter of a cylinder $\left(d\right)=14$

So, the radius of a cylinder $\left(r\right)=\frac{d}{2}=7$

We know that, Volume of a cylinder $\left(V\right)=\pi r^{2}h$

As $r=7,h=8$

  $\begin{array}{l}\therefore V=\frac{22}{7}\times 7^2\times 8\\ \therefore V=1232\end{array}$

Hence, the volume of the cylinder is $1232.$

b.

To determine

To find: The volume of the hemisphere with radius 6.

Answer to Problem 4PSA

The volume of the hemisphere is 452.57.

Explanation of Solution

Given Information:

Radius of a hemisphere $\left(r_1\right)=6$

Formula used:

Volume of a hemisphere $\left(V_1\right)=\frac{2}{3}\pi r_1{}^3$

  $r_1$ is the radius of a hemisphere

Calculation:

The radius of a hemisphere $\left(r_1\right)=6$

We know that, Volume of a hemisphere $\left(V\right)=\frac{2}{3}\pi r_1{}^3$

As $r_1=6$

  $\begin{array}{l}\therefore V=\frac{2}{3}\times \frac{22}{7}\times 6^3\\ \therefore V=452.57\end{array}$

Hence, the volume of the hemisphere is $\mathrm{452.57.}$

c.

To determine

To find: The volume of the plastic used to make the bowl.

Answer to Problem 4PSA

The volume of the plastic used to the bowl is 779.43.

Explanation of Solution

Given Information:

Diameter of a cylinder $\left(d\right)=14$

Height of a cylinder $\left(h\right)=8$

Radius of a hemisphere $\left(r_1\right)=6$

Formula used:

Volume of a cylinder $\left(V\right)=\pi r^{2}h$

  $r\text{and}h$ are the radius and height of a cylinder

Volume of a hemisphere $\left(V_1\right)=\frac{2}{3}\pi r_1{}^3$

  $r_1$ is the radius of a hemisphere

Calculation:

The diameter of a cylinder $\left(d\right)=14$

So, the radius of a cylinder $\left(r\right)=\frac{d}{2}=7$

Volume of the plastic used to make the bowl is $\left(V\text{'}\right)=$ Volume of the cylinder − Volume of the hemisphere

  $\therefore V\text{'}=V-V_1$

We know that,

Volume of a cylinder $\left(V\right)=\pi r^{2}h$

Volume of a hemisphere $\left(V_1\right)=\frac{2}{3}\pi r_1{}^3$

As $r=7,h=8,r_1=6$

  $\begin{array}{l}\therefore V\text{'}=\frac{22}{7}\times 7^2\times 8-\frac{2}{3}\times \frac{22}{7}\times 6^3\\ \therefore V\text{'}=1232-452.57\\ \therefore V\text{'}=779.43\end{array}$

Hence, the volume of the plastic used to the bowl is 779.43.