Chapter 15, Problem 17A

To determine

(a)

The length of side of the given cube.

Answer to Problem 17A

Side length of given cube is $6$ mm.

Explanation of Solution

Given information:

A cube is given whose volume is $216$${\text{mm}}^3$.

Calculation:

As we know that volume of a cube is given by  $V=s^3$

So, side of a cube will be given as  $s=\sqrt[3]{V}$.

  

Here, volume of the given cube is $216$${\text{mm}}^3$. i.e. $V=216$${\text{mm}}^3$.

So, side of the cube will be as follows:

  $\begin{array}{l}s=\sqrt[3]{V}\\ \Rightarrow s=\sqrt[3]{216{\text{ mm}}^3}\text{ {Put }V=216{\text{ mm}}^3\text{}}\\ \Rightarrow s=\sqrt[3]{6\text{ mm }\times 6\text{ mm}\times 6\text{ mm}}\\ \Rightarrow s=6\text{mm }\end{array}$

Hence, side of given cube is $6$ mm.

To determine

(b)

To find the length of side of the given cube.

Answer to Problem 17A

Side length of given cube is $4$ inch.

Explanation of Solution

Given information:

A cube is given whose volume is $64$ cubic inch.

Calculation:

As we know that volume of a cube is given by  $V=s^3$

So, side of a cube will be given as  $s=\sqrt[3]{V}$.

  

Here, volume of the given cube is $64$ cubic inch. i.e. $V=64$ cubic inch.

So, side of the cube will be -

  $\begin{array}{l}s=\sqrt[3]{V}\\ \Rightarrow s=\sqrt[3]{{\text{64 inch}}^3}\text{ {Put }V=64{\text{ inch}}^3\text{}}\\ \Rightarrow s=\sqrt[3]{\text{4 inch }\times \text{4 inch}\times \text{4 inch}}\\ \Rightarrow s=\text{4 inch }\end{array}$

Hence, side of given cube is $4$ inch.

To determine

(c)

The length of side of the given cube.

Answer to Problem 17A

Side length of given cube is $8$ inch.

Explanation of Solution

Given information:

A cube is given whose volume is $512$ cubic inch.

Calculation:

As we know that volume of a cube is given by  $V=s^3$

So, side of a cube will be given as  $s=\sqrt[3]{V}$.

  

Here, volume of the given cube is $512$ cubic inch. i.e. $V=512$ cubic inch.

So, side of the cube will be -

  $\begin{array}{l}s=\sqrt[3]{V}\\ \Rightarrow s=\sqrt[3]{512{\text{ inch}}^3}\text{ {Put }V=512{\text{ inch}}^3\text{}}\\ \Rightarrow s=\sqrt[3]{\text{8 inch }\times 8\text{ inch}\times 8\text{ inch}}\\ \Rightarrow s=8\text{ inch }\end{array}$

Hence, side of given cube is $8$ inch.

To determine

(d)

] length of side of the given cube.

Answer to Problem 17A

Side length of given cube is $10$ mm.

Explanation of Solution

Given information:

A cube is given whose volume is $1000$${\text{mm}}^3$.

Calculation:

As we know that volume of a cube is given by  $V=s^3$

So, side of a cube will be given as  $s=\sqrt[3]{V}$.

  

Here, volume of the given cube is $1000$${\text{mm}}^3$. i.e. $V=1000$${\text{mm}}^2$.

So, side of the cube will be

  $\begin{array}{l}s=\sqrt[3]{V}\\ \Rightarrow s=\sqrt[3]{1000{\text{ mm}}^3}\text{ {Put }V=1000{\text{ mm}}^3\text{}}\\ \Rightarrow s=\sqrt[3]{\text{10 mm }\times 10\text{ mm}\times 10\text{ mm}}\\ \Rightarrow s=10\text{mm }\end{array}$

Hence, side of given cube is $10$ mm.

To determine

(e)

The length of side of the given cube.

Answer to Problem 17A

Side length of given cube is $1$ inch.

Explanation of Solution

Given information:

A cube is given whose volume is $1$ cubic inch.

Calculation:

As we know that volume of a cube is given by -

  $V=s^3$

So, side of a cube will be given as -

  $s=\sqrt[3]{V}$.

  

Here, volume of the given cube is $1$ cubic inch. i.e. $V=1$ cubic inch.

So, side of the cube will be -

  $\begin{array}{l}s=\sqrt[3]{V}\\ \Rightarrow s=\sqrt[3]{1{\text{ inch}}^3}\text{ {Put }V=1{\text{ inch}}^3\text{}}\\ \Rightarrow s=\sqrt[3]{\text{1 inch }\times 1\text{ inch}\times 1\text{ inch}}\\ \Rightarrow s=1\text{ inch }\end{array}$

Hence, side of given cube is $1$ inch.