Question

homework: unit 3 - geometry question 34, 6.5.5 part 1 of 2 hw score: 74.14%, 43 of 58 points points: 0 of 1 find the volume of the solid (a cone with height 9 yd and radius 2 yd). 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.)

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 \( r = 2 \) yd and the height \( h = 9 \) yd.

Step3: Substitute the values into the formula

Substitute \( r = 2 \) and \( h = 9 \) into the volume formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi(2)^2(9)\\ &=\frac{1}{3}\pi\times4\times9\\ &=\frac{1}{3}\times36\pi\\ & = 12\pi \end{align*}$$

\]

Answer:

The exact value of the volume is \( 12\pi \) cubic yards.