Chapter 4.1, Problem 58IP

a.

To determine

To write: an equation showing the relationship between side length s and volume V of a cube.

Answer to Problem 58IP

  $V=x^3$ .

Explanation of Solution

Given information: The volume of a cube equals the side length cubed.

Calculation:

The below equation showing the relationship between side length s and volume V of a cube.

  $V=x^3$ .

b.

To determine

To make: a table of values showing the volume of a cube with side lengths of 1, 2, 4, 8, 16 centimeters.

Answer to Problem 58IP

Explanation of Solution

Given information: The volume of a cube equals the side length cubed.

Calculation:

The table showing the volume of a cube with side lengths of 1, 2, 4, 8, 16 centimeters is shown below.

Side s (centimeters)	$s^3$	Volume ( $V=s^3$ ) centimeter cube
1	$1^3$	1
2	$2^3$	8
4	$4^3$	64
8	$8^3$	512
16	${16}^3$	4096

c.

To determine

To make: a conjecture about the change in volume when the side length of a cube is doubled.

Answer to Problem 58IP

Whenthe side length of a cube is doubled, the volume becomes 8 times.

Explanation of Solution

Given information: The volume of a cube equals the side length cubed.

Calculation:

Let s is the side of a cube, and then volume of the cube is:

  $V_s=s^3$ .

If the side length is doubled then the new side length will be 2s, so when the side length is 2s, then the volume will be

  $\begin{array}{l}$ V_{2s}={(2s)}^3=8s^3=8V_s$V_{2s}=8V_s\end{array}$ .

Hence, when the side length of a cube is doubled, the volume becomes 8 times.