Chapter 12, Problem 2RP

a

To determine

To calculate : The volume of the given Cube.

Answer to Problem 2RP

The volume of the cube with side length 8 units $\left(V\right)=512{\text{ units}}^3$

Explanation of Solution

Given information:

Side length of the cube $\left(a\right)=8\text{ units}$

Formula used:

Volume of a cube with side length $a$ units is, $\text{V}=a^3{\text{ units}}^3$

Calculation:

  $\text{V}=a^3=8^3=512{\text{ units}}^3$

  

b

To determine

To calculate : The volume of a rectangular box or Cuboid.

Answer to Problem 2RP

The volume of the rectangular $\left(V\right)=108{\text{ units}}^3$

Explanation of Solution

Given information:

Length $\left(l\right)=3\text{ units}$

Breadth $\left(b\right)=4\frac{1}{2}\text{ units}$

Height $\left(h\right)=8\text{ units}$

Formula used:

Volume of a rectangular box (cuboid) that measures length $\left(l\right)$ by breadth $\left(b\right)$ by height $\left(h\right)$

  $\left(\text{V}\right)=l\times b\times h{\text{ units}}^3$

Calculation:

We have,

  $\left(l\right)=3\text{ units}$ ,

  $\left(b\right)=4\frac{1}{2}=4+\frac{1}{2}=\frac{8+1}{2}=\frac{9}{2}\text{ units}$

  $\left(h\right)=8\text{ units}$

  $\begin{array}{c}\text{Volume }\left(\text{V}\right)=l\times b\times h\\ \text{=3}\times \frac{9}{2}\times \text{8 }\\ =3\times 9\times 4\\ =108{\text{ units}}^3\end{array}$

  

c

To determine

To calculate : The volume of the cylinder.

Answer to Problem 2RP

The volume of the cylinder with a radius 7 units and a height of 2 units is $\left(\text{V}\right)=98{\text{π units}}^3$

Explanation of Solution

Given information:

Radius $\left(r\right)=7\text{ units}$

Height $\left(h\right)=2\text{ units}$

Formula used:

Volume of the cylinder with radius $\left(r\right)$ and height $\left(h\right)$ is, $\text{V}=\text{π}{r}^2\times h{\left(\text{units}\right)}^3$

Calculation:

  $\begin{array}{c}\text{Volume }\left(\text{V}\right)=\text{π}{r}^2\times h\\ =\text{π}\times 7^2\times 2\\ =\text{π}\times 49\times 2\\ =98\text{π }{\left(\text{units}\right)}^3\end{array}$

  

d

To determine

To calculate : The volume of the Pyramid.

Answer to Problem 2RP

The volume of the Pyramid with a height of 5 units and a base are of 12 units is $\left(\text{V}\right)=20{\text{ units}}^3$

Explanation of Solution

Given information:

Height $\left(h\right)=5\text{ units}$

Base area $\left(A\right)=12{\text{ units}}^2$

Formula used:

Volume of a pyramid with base area $\left(A\right)$ and height $\left(h\right)$ is, $\text{V}=\frac{1}{3}\times \text{A}\times h{\left(\text{units}\right)}^3$

Calculation:

  $\begin{array}{c}\text{Volume }\left(\text{V}\right)=\text{V}=\frac{1}{3}\times \text{A}\times h\\ =\frac{1}{3}\times 12\times 5\\ =20{\left(\text{units}\right)}^3\end{array}$

  

e

To determine

To calculate : The volume of the Prism.

Answer to Problem 2RP

The volume of the prism with base area $12{\text{ units}}^2$ and height $5\text{ units}$

  $\left(V\right)=60{\text{ units}}^3$

Explanation of Solution

Given information:

Base area $\left(A\right)=12{\text{ units}}^2$

Height $\left(h\right)=5\text{ units}$

Formula used:

The volume of the prism with base area $\left(A\right)$ and height $\left(h\right)$ is, $V=A\times h{\text{ units}}^3$

Calculation:

  $\begin{array}{c}\text{Volume }\left(V\right)=A\times h{\text{ units}}^3\\ =12\times 5\\ =60{\left(\text{units}\right)}^3\end{array}$

  

f

To determine

To calculate : The volume of the Sphere.

Answer to Problem 2RP

The volume of the sphere with radius 2 units is $\left(V\right)=\text{10}{\text{.67π units}}^3$

Explanation of Solution

Given information:

Radius of the sphere $\left(r\right)=2\text{ units}$

Formula used:

Volume of the sphere with radius $r\text{ units}$ is $\left(V\right)=\frac{4}{3}\times \text{π}\times r^3{\text{ units}}^3$

Calculation:

  $\begin{array}{c}\text{Volume }\left(V\right)=\frac{4}{3}\times \text{π}\times r^3\\ =\frac{4}{3}\times \text{π}\times 2^3\\ =\frac{32}{3}\text{π}\\ =\text{10}\text{.67π }{\left(\text{units}\right)}^3\end{array}$