Chapter 12.5, Problem 14WE

To determine

To find: The total weight the snow man.

Answer to Problem 14WE

The total weight of the snow man is $48\text{kg}$ .

Explanation of Solution

Given information:

The diameter of the ballsis $30\text{cm,}40\text{cm}$ , and $50\text{cm}$ .The weight of the head is $6\text{kg}$ .

Calculation:

The weight of the ball is proportional to the cube of its diameter. The diameter of the mid ball is $30\text{cm}$ and diameter of the head ball is $40\text{cm}$ .

Calculate the weight of the mid ball.

  $\begin{array}{c}\frac{\text{Weight}\text{of the}\text{mid}\text{part}}{\text{Weight}\text{of the}\text{head}}={\left(\frac{40}{30}\right)}^3\\ \frac{\text{Weight}\text{of the}\text{mid}\text{part}}{6}={\left(\frac{4}{3}\right)}^3\\ \text{Weight}\text{of the}\text{mid}\text{part}=\frac{64}{27}\times 6\\ =14\cdot 2\text{kg}\end{array}$

The weight of the ball is proportional to the cube of its diameter. The diameter of the bottom ball is $50\text{cm}$ and the diameter of head ball is $30\text{cm}$ .

Calculate the weight of the bottom ball.

  $\begin{array}{c}\frac{\text{Weight}\text{of the}\text{bottom}\text{part}}{\text{Weight}\text{of the}\text{head}}={\left(\frac{50}{30}\right)}^3\\ \frac{\text{Weight}\text{of}\text{the}\text{bottom}\text{part}}{6}={\left(\frac{4}{3}\right)}^3\\ \text{Weight}\text{of the}\text{bottom}\text{part}=\frac{125}{27}\times 6\\ =27\cdot 78\text{kg}\end{array}$

The total weight of the snow man is sum of the weight of three balls.

  $\begin{array}{c}\text{Total}\text{weight}=6+14\cdot 2+27\cdot 8\\ =48\text{kg}\end{array}$

Therefore,the totalweight ofthe snow man is $48\text{kg}$ .