Chapter 12.5, Problem 33PPS

To determine

To determine the diameter of the base of the cone.

Answer to Problem 33PPS

  $14\text{ centimeter}$

Explanation of Solution

Given:

Volume of cone $=196\pi {\text{ inches}}^3$

Height of cone $=12\text{ inches}$

Formula used:

Volume of the cone, $V=\frac{1}{3}\pi r^{2}h$

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Calculation:

Given, volume of cone $=196\pi {\text{ inches}}^3.$

Height of cone $=12\text{ inches}\text{.}$

To determine the values of diameter of the cone,

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

  $\Rightarrow$ The values of radius of the cone $=\sqrt{\frac{\text{volume}\times 3}{\pi h}}$

  $\Rightarrow$ The values of radius of the cone $=\sqrt{\frac{196\pi \times 3}{\pi \times 12}}$

  $\Rightarrow$ The values of radius of the cone $=\sqrt{49}$

  $\Rightarrow$ The values of radius of the cone $=7\text{ centimeter}$

  $\Rightarrow$ The values of diameter of the cone $=2\times 7\text{ centimeter}$

  $\Rightarrow$ The values of diameter of the cone $=14\text{ centimeter}$

Conclusion:

Therefore, the values of diameter of the cone $=14\text{ centimeter}$ .