find the volume of a right circular cone that has a height of 19.9 cm and a base with a radius of 9.6 cm…

Explanation:

Step1: Recall volume formula

The volume formula for a right - circular cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

Step2: Substitute given values

Given $r = 9.6$ cm and $h=19.9$ cm. Substitute into the formula: $V=\frac{1}{3}\pi(9.6)^{2}(19.9)$. First, calculate $(9.6)^{2}=92.16$. Then $V=\frac{1}{3}\pi\times92.16\times19.9$. $\frac{1}{3}\times92.16 = 30.72$. So $V = 30.72\pi\times19.9$. $30.72\times19.9 = 611.328$. So $V=611.328\pi$.

Step3: Calculate the value

Using $\pi\approx3.14$, we have $V\approx611.328\times3.14 = 1919.57992$.

Step4: Round the answer

Rounding to the nearest tenth, $V\approx1919.6$ $cm^{3}$.

Answer:

$1919.6$ $cm^{3}$