Chapter 12.6, Problem 48HP

To determine

Write the ratio of the volume of a sphere with radius r and volume of a cylinder with radius r and height $2r$ and compare them.

Answer to Problem 48HP

The volume of the cylinder will be $1.5$ times larger.

Explanation of Solution

Given:

It is given in the question that the radius of sphere is r and the radius of the cylinder is r and height is $2r$ .

Concept Used:

In this, use the concept of using the formulas of sphere and cylinder i.e. $V_{sphere}=\frac{4}{3}\pi r^3$ & $V_{cylinder}=\pi r^{2}h,$

The volume of the cylinder is $\pi r^{2}h$ and the volume of sphere is $\frac{4}{3}\pi r^3$ .

Compare them in the ratio:

  $\begin{array}{l}\frac{4}{3}\pi r^3:\pi r^{2}h\\ \frac{4}{3}\pi r^3:\pi r^2(2r)\\ \frac{4}{3}\pi r^3:2\pi r^3\\ \frac{4}{3}:2\\ 1:\frac{3}{2}(Multiplyingbothsidesby\frac{3}{4})\end{array}$