Chapter 12.4, Problem 30HP

To determine

To explain: effect on the volume of a cone changing radius or changing the height.

Answer to Problem 30HP

Changing the radius has a greater effect on the volume of a cone.

Explanation of Solution

Given:

Condition: effect on the volume of a cone changing radius or changing the height

volume of cone is calculated as,

  $V=\frac{1}{3}\pi r^{2}h$

volume $\left(V\right)$ cone is calculated as,

  $V=\frac{1}{3}\pi r^{2}h$

So,

  $\begin{array}{l}V\alpha r^2\mathrm{...}\left(i\right)\\ V\alpha h\mathrm{...}\left(ii\right)\end{array}$

So the volume of cone is directly proportional to the square of radius and height.

So changing the radius has a greater effect on the volume of a cone.

Conclusion:

Thus, changing the radius has a greater effect on the volume of a cone.