Chapter 12.6, Problem 43PPS

To determine

Describe the change affects the surface area and the volume of the sphere when its radius is divided by $3$ .

Answer to Problem 43PPS

Surface area of the sphere is decreased by $9$ times

And, the volume of the sphere is decreased by $27$ times.

Explanation of Solution

Given information:

It is given in the question that, the radius of the sphere is $12cm$ .

Formula used:

  $\begin{array}{l}Surfaceareaofsphereis=4\pi r^2\hfill \\ Volumeofthesphere =\frac{4}{3}\pi r^3\hfill \end{array}$

Calculation:

For the sphere having radius $12cm$ is,

  $\begin{array}{l}Surfaceareaofsphereis=4\pi r^2\hfill \\ \begin{array}{l}=4*\frac{22}{7}*12*12\\ =\frac{12672}{7}\\ =1810.28\end{array}\hfill \end{array}$

  $\begin{array}{l}Volumeofthesphere =\frac{4}{3}\pi r^3\\ =\frac{4}{3}*\frac{22}{7}*12*12*12\\ =\frac{152064}{7}\\ =21723.42\end{array}$

For the sphere having radius $12cm*\frac{1}{3}=4cm$ is,

  $\begin{array}{l}Surfaceareaofsphereis=4\pi r^2\hfill \\ \begin{array}{l}=4*\frac{22}{7}*\left(12*\frac{1}{3}\right)*\left(12*\frac{1}{3}\right)\\ =\frac{12672}{7}*\frac{1}{9}\\ =1810.28*\frac{1}{9}\end{array}\hfill \end{array}$

  $\begin{array}{l}Volumeofthesphere =\frac{4}{3}\pi r^3\\ =\frac{4}{3}*\frac{22}{7}*\left(12*\frac{1}{3}\right)*\left(12*\frac{1}{3}\right)*\left(12*\frac{1}{3}\right)\\ =\frac{152064}{7}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}\\ =21723.42*\frac{1}{27}\end{array}$

Since from the above solution that when we divide the radius by $3$ then the,

Surface area of the sphere is decreased by $9$ times

And, the volume of the sphere is decreased by $27$ times.