Question

find the volume of a right circular cone that has a height of 13.8 ft and a base with a radius of 7.8 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a right circular 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: Substitute the given values into the formula

We are given that \( r = 7.8\) ft and \( h=13.8\) ft. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\pi(7.8)^{2}(13.8) \)

Step3: Calculate the value of \( (7.8)^{2} \)

First, calculate \( 7.8\times7.8 = 60.84 \)

Step4: Multiply the values inside the formula

Now, multiply \( 60.84\times13.8 \). Let's calculate that: \( 60.84\times13.8=60.84\times(10 + 3+0.8)=60.84\times10+60.84\times3 + 60.84\times0.8=608.4+182.52+48.672 = 839.592\)

Step5: Multiply by \( \frac{1}{3}\pi \)

Now, multiply \( 839.592\times\frac{1}{3}\pi=\frac{839.592}{3}\pi = 279.864\pi\)

Step6: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( 279.864\times3.14159\approx279.864\times3.14159\approx900.2 \) (rounded to the nearest tenth)

Answer:

\( 900.2 \) cubic feet