Chapter 15, Problem 1A

A sphere has a volume, V, of 12.249 cu in. Use the formula $D=\sqrt[3]{\frac{V}{0.5236}}$to determine the diameter, D, of the sphere.

To determine

The length of diameter of the given sphere.

Answer to Problem 1A

Diameter length of given sphere is $2.86$ inch.

Explanation of Solution

Given information:

A sphere is given whose volume is $12.249$ 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 $12.249$ cubic inch. i.e. $V=12.249$ cubic inch.

So, diameter of the sphere will be -

  $\begin{array}{l}D=\sqrt[3]{\frac{V}{0.5236}}\\ \Rightarrow D=\sqrt[3]{\frac{12.249}{0.5236}{\text{inch}}^3}\text{ {Put }V=12.249{\text{ inch}}^3\text{}}\\ \Rightarrow D=\sqrt[3]{23.393812{\text{inch}}^3}\\ \Rightarrow D=2.86\text{ inch }\end{array}$

Hence, diameter of given sphere is $2.86$ inch.