Chapter 12.4, Problem 43HP

a.

To determine

To describe: The possible dimension of the figure if it is a rectangular prism.

Explanation of Solution

Given information : A cylinder can with radius $r=2in$ , height $h=5in$ is given. This volume of the container is thrice the volume of the can.

Formula used : The volume of a cylinder can is $V=\pi r^{2}h$ .

Calculation : Calculate the volume of the container.

  $\begin{array}{l}{V}_c=3V=3\pi r^{2}h\\ =3\times \pi \times 2^2\times 5\\ =188.5i{n}^3\end{array}$

Now, describing the possible dimensions in each of the following cases.

The volume of a rectangular prism is $V=lwh$ .

Calculate the possible dimensions of the rectangular prism.

  $\begin{array}{l}V=lwh=188.5i{n}^3\\ lwh=188.5\end{array}$

The possible combination of dimensions can be $l=6in,w=4in,h=7.85in$ .

b.

To determine

To describe: The possible dimension of the figure if it is a square prism.

Explanation of Solution

Given: The container is a Square prism.

Formula used : The volume of a square prism.is $V=a^{2}h$ .

Calculation : Calculate the possible dimensions of the square prism.

  $\begin{array}{l}V=a^{2}h=188.5i{n}^3\\ a^{2}h=188.5\end{array}$

The possible combination of dimensions can be $a=6in,h=5.24in$ .

c.

To determine

To describe: The possible dimension of the figure if it is a right triangular prism.

Explanation of Solution

Given: The container is a right triangular prism.

Formula used : The volume of a right triangular prism is $V=\frac{lw}{2}h$ .

Calculation : Calculate the possible dimensions of the right triangular prism.

  $\begin{array}{l}V=\frac{lw}{2}h=188.5i{n}^3\\ \frac{lw}{2}h=188.5\end{array}$

The possible combination of dimensions can be $l=6in,w=8in,h=7.85in$ .