Question

volume of a cone level 1
score:5/15 penalty:1 off
question
find the volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of 14.4 ft. round your answer to the nearest tenth of a cubic foot.
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answer attempt 1 out of 2
ft³
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Explanation:

Step1: Find the radius

The diameter is 14.4 ft, so the radius \( r=\frac{14.4}{2}=7.2 \) ft.

Step2: Recall the volume formula for a cone

The volume \( V \) of a right circular cone is given by \( V = \frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step3: Substitute the values

We know \( r = 7.2 \) ft, \( h = 2.7 \) ft, and \( \pi\approx3.14159 \).
So \( V=\frac{1}{3}\times3.14159\times(7.2)^{2}\times2.7 \)
First, calculate \( (7.2)^{2}=51.84 \)
Then, \( \frac{1}{3}\times3.14159\times51.84\times2.7 \)
\( \frac{1}{3}\times2.7 = 0.9 \)
So \( V = 3.14159\times51.84\times0.9 \)
\( 3.14159\times51.84 = 162.9911 \) (approx)
Then \( 162.9911\times0.9 = 146.692 \) (approx)

Step4: Round to the nearest tenth

Rounding 146.692 to the nearest tenth gives 146.7.

Answer:

146.7