Question

find the volume of a cone with a height of 7 ft and a base diameter of 6 ft. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius of the base

The diameter of the base is 6 ft, so the radius \( r \) is half of the diameter.
\( r = \frac{6}{2} = 3 \) ft.

Step2: 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, \( h \) is the height, and \( \pi \) is approximately 3.14.

Step3: Substitute the values into the formula

We know that \( r = 3 \) ft, \( h = 7 \) ft, and \( \pi = 3.14 \). Substituting these values into the formula:
\[

$$\begin{align*} V &= \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \\ &= \frac{1}{3} \times 3.14 \times 9 \times 7 \\ \end{align*}$$

\]

Step4: Calculate the volume

First, calculate \( 3.14 \times 9 = 28.26 \). Then, multiply by 7: \( 28.26 \times 7 = 197.82 \). Finally, multiply by \( \frac{1}{3} \): \( \frac{1}{3} \times 197.82 = 65.94 \).

Answer:

\( 65.94 \) cubic feet (or \( 65.94 \text{ ft}^3 \))