Question

calculator
what is the exact volume of the cone?
80π ft³
\\(\frac{400}{3}\\)π ft³
400π ft³
\\(\frac{4187}{10}\\)π ft³
(image of a cone with height 16 ft and radius 5 ft)

Explanation:

Step1: Recall the volume formula for 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 \( r = 5\space ft \) and the height \( h=16\space ft \).

Step3: Substitute the values into the formula

Substitute \( r = 5 \) and \( h = 16 \) into the formula \( V=\frac{1}{3}\pi r^{2}h \):
\[

$$\begin{align*} V&=\frac{1}{3}\pi\times(5)^{2}\times16\\ &=\frac{1}{3}\pi\times25\times16\\ &=\frac{400}{3}\pi \end{align*}$$

\]

Answer:

\(\frac{400}{3}\pi\space ft^{3}\) (corresponding to the option \(\frac{400}{3}\pi\space ft^{3}\))