Chapter 14, Problem 19A

To determine

(a)

The length of diameter of the given sphere.

Answer to Problem 19A

Diameter length of given sphere is $3$ inch.

Explanation of Solution

Given information:

A sphere is given whose volume is $14.1372$ cubic inch.

Calculation:

As we know that volume of a sphere is given by -  $V=\frac{\pi \times D^3}{6}$

So, diameter length of the sphere will be given as -  $D=\sqrt[3]{\frac{V}{0.5236}}$

  

Here, volume of the given sphere is $14.1372$ cubic inch. i.e. $V=14.1372$ cubic inch.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{14.1372}{0.5236}{\text{inch}}^3}\text{ {Put }V=14.1372{\text{ inch}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{27{\text{inch}}^3}\\ \Rightarrow D=\sqrt[3]{\text{3 inch }\times 3\text{ inch}\times 3\text{ inch}}\\ \Rightarrow D=3\text{ inch }\end{array}$

Hence, diameter of given sphere is $3$ inch.

To determine

(b)

The length of diameter of the given sphere.

Answer to Problem 19A

Diameter length of given sphere is $6$ mm.

Explanation of Solution

Given information:

A sphere is given whose volume is $113.0976$ cubic mm.

Calculation:

As we know that volume of a sphere is given by -  $V=\frac{\pi \times D^3}{6}$

So, diameter length of the sphere will be given as -  $D=\sqrt[3]{\frac{V}{0.5236}}$

  

Here, volume of the given sphere is $113.0976$ cubic mm. i.e. $V=113.0976$ cubic mm.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{113.0976}{0.5236}{\text{mm}}^3}\text{ {Put }V=113.0976{\text{ mm}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{216{\text{mm}}^3}\\ \Rightarrow D=\sqrt[3]{\text{6 mm }\times 6\text{ mm}\times 6\text{ mm}}\\ \Rightarrow D=6\text{ mm }\end{array}$

Hence, diameter of given sphere is $6$ mm.

To determine

(c)

To find the length of diameter of the given sphere.

Answer to Problem 19A

Diameter length of given sphere is $2$ inch.

Explanation of Solution

Given information:

A sphere is given whose volume is $4.1888$ cubic inch.

Calculation:

As we know that volume of a sphere is given by -  $V=\frac{\pi \times D^3}{6}$

So, diameter length of the sphere will be given as -  $D=\sqrt[3]{\frac{V}{0.5236}}$

  

Here, volume of the given sphere is $4.1888$ cubic inch. i.e. $V=4.1888$ cubic inch.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{4.1888}{0.5236}{\text{inch}}^3}\text{ {Put }V=4.1888{\text{ inch}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{8{\text{inch}}^3}\\ \Rightarrow D=\sqrt[3]{\text{2 inch }\times 2\text{ inch}\times 2\text{ inch}}\\ \Rightarrow D=2\text{ inch }\end{array}$

Hence, diameter of given sphere is $2$ inch.

To determine

(d)

The length of diameter of the given sphere.

Answer to Problem 19A

Diameter length of given sphere is $1$ inch.

Explanation of Solution

Given information:

A sphere is given whose volume is $0.5236$ cubic inch.

Calculation:

As we know that volume of a sphere is given by -  $V=\frac{\pi \times D^3}{6}$

So, diameter length of the sphere will be given as -  $D=\sqrt[3]{\frac{V}{0.5236}}$

  

Here, volume of the given sphere is $0.5236$ cubic inch. i.e. $V=0.5236$ cubic inch.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{0.5236}{0.5236}{\text{inch}}^3}\text{ {Put }V=0.5236{\text{ inch}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{1{\text{inch}}^3}\\ \Rightarrow D=\sqrt[3]{\text{1 inch }\times 1\text{ inch}\times 1\text{ inch}}\\ \Rightarrow D=1\text{ inch }\end{array}$

Hence, diameter of given sphere is $1$ inch.

To determine

(e)

The length of diameter of the given sphere.

Answer to Problem 19A

Diameter length of given sphere is $10$ mm.

Explanation of Solution

Given information:

A sphere is given whose volume is $523.6$ cubic mm.

Calculation:

As we know that volume of a sphere is given by -  $V=\frac{\pi \times D^3}{6}$

So, diameter length of the sphere will be given as -  $D=\sqrt[3]{\frac{V}{0.5236}}$

  

Here, volume of the given sphere is $523.6$ cubic mm. i.e. $V=523.6$ cubic mm.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{523.6}{0.5236}{\text{mm}}^3}\text{ {Put }V=523.6{\text{ mm}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{1000{\text{mm}}^3}\\ \Rightarrow D=\sqrt[3]{\text{10 mm }\times 10\text{ mm}\times 10\text{ mm}}\\ \Rightarrow D=10\text{ mm }\end{array}$

Hence, diameter of given sphere is $10$ mm.