Question

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.
answer attempt 2 out of 2
900.7 ft³ submit answer

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 \( 7.8^2 \):

$$ 7.8^2=7.8\times7.8 = 60.84 $$

Step4: Multiply the values inside the formula

Now, multiply \( 60.84 \) by \( 13.8 \):

$$ 60.84\times13.8 = 60.84\times(10 + 3+ 0.8)=60.84\times10+60.84\times3 + 60.84\times0.8=608.4+182.52+48.672 = 839.592 $$

Then multiply by \( \frac{1}{3}\pi \):

$$ V=\frac{1}{3}\pi\times839.592=\pi\times279.864 $$

Using \( \pi\approx3.14159 \), we have:

$$ V\approx3.14159\times279.864 $$

Step5: Perform the final multiplication and round

Calculate \( 3.14159\times279.864 \approx 880.7 \) (rounded to the nearest tenth)

Answer:

\( 880.7 \)