Chapter 12.8, Problem 5CYU

To determine

Find the volume of the larger ball.

Answer to Problem 5CYU

  $220,893.2c{m}^3$

Explanation of Solution

Given:

The ratio of the diameters is 15:11.The diameter of the smaller ball is 55 cm.

Formula Used:

Two solids are similar if they have the same shape and the ratios of their corresponding linear measures are equal.

The Volume of sphere is :

  $V=\frac{4}{3}\pi r^3$ ; where r is the radius of the sphere.

Calculation:

Given:

Diameter of smaller ball =

  $\begin{array}{l}{d}_1=55cm\\ \Rightarrow r_1=\frac{55}{2}=27.5cm\end{array}$

  $\begin{array}{l}\frac{d_1}{d_2}=\frac{11}{15}\\ \Rightarrow \frac{55}{d_2}=\frac{11}{15}\mathrm{...........}[d_1=55cm]\\ \Rightarrow 15\cdot 55=11d_2\mathrm{.....}[\text{multiply each side by 15}{d}_2]\\ \Rightarrow d_2=\frac{15\cdot 55}{11}\mathrm{........}[\text{divide each side by 15]}\\ \Rightarrow d_2=75\\ \Rightarrow r_2=\frac{75}{2}=37.5cm\end{array}$ ; where $d_2$ is the diameter of the larger ball

The volume of the larger ball:

  $\begin{array}{l}{V}_2=\frac{4}{3}\pi r_2{}^3\\ \Rightarrow V_2=\frac{4}{3}\pi {(}^{37.5}\\ \Rightarrow V_2\approx 220,893.2c{m}^3\end{array}$