Chapter 12.5, Problem 13WE

To determine

To find: Theweight of the larger ball.

Answer to Problem 13WE

The weight of the larger ball is $18\cdot 5\text{kg}$ .

Explanation of Solution

Given information:

The radius of the small ball is 6 cm and the radius of the larger ball is 10 cm. The weight of the smaller ballis $4\text{kg}$ .

Calculation:

The weight of the ball is proportional to the cube of radius. Write the ratio of the weight of the larger ball to the smaller ball.

  $\begin{array}{c}\frac{\text{Weight}\text{of}\text{the}\text{larger}\text{ball}}{\text{Weight}\text{of}\text{the}\text{smaller}\text{ball}}={\left(\frac{10}{6}\right)}^3\\ \frac{\text{Weight}\text{of}\text{the}\text{larger}\text{ball}}{4}={\left(\frac{5}{3}\right)}^3\\ \text{Weight}\text{of}\text{the}\text{larger}\text{ball}=\frac{125}{127}\times 4\\ =18\cdot 5\text{kg}\end{array}$

Therefore,the weight of the larger ballis $18\cdot 5\text{kg}$ .