Question

question 3 3 of 6 find the volume of the solid shown below. use 3.14 for π and round your answer to the nearest tenth of a cubic yard. the volume of the solid is ______ cubic yards. the solution is

Explanation:

Step1: Recall the formula for the volume of 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 \( r = 3 \) yards and the height \( h=8 \) yards. We are given that \( \pi = 3.14 \).

Step3: Substitute the values into the formula

Substitute \( r = 3 \), \( h = 8 \) and \( \pi=3.14 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times3.14\times(3)^{2}\times8\\ &=\frac{1}{3}\times3.14\times9\times8\\ &= 3.14\times3\times8\\ &=3.14\times24 \end{align*}$$

\]

Step4: Calculate the result

\( 3.14\times24 = 75.36 \)

Step5: Round to the nearest tenth

Rounding \( 75.36 \) to the nearest tenth gives \( 75.4 \).

Answer:

\( 75.4 \)