Question

find the volume of the solid. for formulas containing π, give the exact answer and then an approximation using \\(\frac{22}{7}\\) for π. the exact value of the volume is \\(\square\\) (simplify your answer. type an exact answer in terms of π.) (image shows a cone with height 9 yd and radius 4 yd)

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), 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 \( r = 4\) yd and the height \( h=9\) yd.

Step3: Substitute the values into the formula

Substitute \( r = 4 \) and \( h = 9 \) into the formula \( V=\frac{1}{3}\pi r^{2}h \):
\[

$$\begin{align*} V&=\frac{1}{3}\pi\times(4)^{2}\times9\\ &=\frac{1}{3}\pi\times16\times9\\ &=\pi\times16\times3\\ & = 48\pi \end{align*}$$

\]

Answer:

\( 48\pi \) cubic yards