Question

1. find the volume of the cone. round to the nearest hundredth. 22 m 7 m type a response

Explanation:

Step1: Recall the formula for the volume of a cone

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

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 7\space m \) and the height \( h=22\space m \).

Step3: Substitute the values into the formula

Substitute \( r = 7 \) and \( h = 22 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(7)^{2}\times22\\ &=\frac{1}{3}\times\pi\times49\times22\\ &=\frac{1078\pi}{3} \end{align*}$$

\]

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\[

$$\begin{align*} V&\approx\frac{1078\times3.14159}{3}\\ &\approx\frac{3386.74402}{3}\\ &\approx1128.91 \end{align*}$$

\]

Answer:

The volume of the cone is approximately \( 1128.91\space m^{3} \)