Chapter 4.5, Problem 31IP

To determine

To find : how many tons of sand is being used for the volleyball

Answer to Problem 31IP

131 tons of sand is being used for the volleyball

Explanation of Solution

Given information :

  $1.6\cdot {10}^3$ cubic feet of sand that weight 95 pounds per cubic foot and $1.25\cdot {10}^3$ cubic feet of sand that weight is 88 pounds per cubic foot

Calculation :

The weight of sand being used in $1.6\cdot {10}^3$ cubic feet is

  $\begin{array}{l}=1.6\cdot {10}^3{\text{ft}}^3\cdot \frac{95\text{lbs}}{{\text{ft}}^3}\\ =1.6\cdot {10}^3\cdot 95\text{lbs}\\ \text{=152}\cdot {\text{10}}^3\text{lbs}\end{array}$

The weight of sand being used $1.25\cdot {10}^3$ cubic feet is

  $\begin{array}{l}=1.25\cdot {10}^3{\text{ft}}^3\cdot \frac{\text{88lbs}}{{\text{ft}}^3}\\ =1.25\cdot {10}^3\cdot 88\text{lbs}\\ \text{=110}\cdot {\text{10}}^3\text{lbs}\end{array}$

The total weight of sand being used is

  $\begin{array}{l}=152\cdot {10}^3\text{lbs+110}\cdot {\text{10}}^3\text{lbs}\\ =\text{262}\cdot {\text{10}}^3\text{lbs}\end{array}$

Therefore, $\text{262}\cdot {\text{10}}^3\text{lbs}$ is equal to

  $\begin{array}{l}262\cdot {10}^3\text{lbs}\\ \text{=262}\cdot {10}^3\frac{1\text{ tons}}{2000}\\ =131\text{ tons}\end{array}$

Hence,131 tons of sand is being used for the volleyball.