Chapter 12.7, Problem 5P

To determine

To calculate: The radius of a cylinder of equal volume whose height is 96 cm . If a cylinder of radius is 6 cm height is 24 cm . also given the height of cylinder volume is inversely proportional to the square of radius.

Answer to Problem 5P

The radius of ball is $r=3$ .

Explanation of Solution

Given information:

The the radius of a cylinder of equal volume is inversely proportional to the square of the radius

Let , Radius = r

Height = h

Let k be a constant

  $h=\frac{k}{r^2}$ ............. $\left(1\right)$

Also given, cylinder of radius is 6cm and height 24cm

Cylinder of radius is 6 cm and height 24 cm.

Put the value of r and h to equation 1 to get value of k .

  $\begin{array}{l}24=\frac{k}{{\left(6\right)}^2}\\ 24=\frac{k}{36}\end{array}$

Solve further to get k ,

Put the value of h and k in equation 1 to get value of r .

  $h=\frac{k}{r^2}$

  $\begin{array}{l}96=\frac{k}{r^2}\\ 96=\frac{24\times 36}{r^2}\end{array}$

Solve further to get r .

  $\begin{array}{l}{r}^2=\sqrt{\frac{24\times 36}{96}}\\ r=\sqrt{9}\\ r=3\end{array}$