Chapter 3.1, Problem 60PS

Solution

The radius of the shot used in men’s shot put.

  $6\text{ centimeters}$

Given:

The shot used in men’s shot put has a volume of about 905 cubic centimeters.

Concept Used:

• The even inter root of a number is defined for positive values only that are greater than or equal to 0.
• The odd integer root of all real numbers is defined.
• Power of a power property: ${\left(x^a\right)}^b=x^{a\cdot b}$
• The equivalent expression in rational exponent for any nth radical is given by, $\sqrt[n]{a}=a^{\frac{1}{n}}$ .

Calculation:

In order to find the radius of the shot used in the men’s shot put, substitute $V=905$ into the volume of sphere formula and solve for r as shown below

  $\begin{array}{c}V=\frac{4}{3}\pi r^3\\ 905=\frac{4}{3}\pi r^3\\ \frac{3}{4}\cdot 905=\frac{3}{4}\cdot \frac{4}{3}\pi r^3\\ \frac{2715}{4}=\pi r^3\\ \frac{2715}{4\pi }=r^3\\ r=\sqrt[3]{\frac{2715}{4\pi }}\\ r\approx 6\end{array}$

Thus, the radius of the shot is about 6 centimeters.