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 \\(\boxed{}\\) (simplify your answer. type an exact answer in terms of π.) diagram of a cone with height 8 yd and radius 3 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 \( r = 3\) yd and the height \( h=8\) yd.

Step3: Substitute the values into the formula

Substitute \( r = 3\) and \( h = 8\) into the formula \( V=\frac{1}{3}\pi r^{2}h \):
\[

$$\begin{align*} V&=\frac{1}{3}\pi\times(3)^{2}\times8\\ &=\frac{1}{3}\pi\times9\times8\\ &= 3\pi\times8\\ &= 24\pi \end{align*}$$

\]

Answer:

\( 24\pi \) cubic yards