Question

volume of a cone level 1
score:8/15 penalty:1 off
question
find the volume of a right circular cone that has a height of 18.8 in and a base with a diameter of 14.3 in. round your answer to the nearest tenth of a cubic inch.
answer attempt 1 out of 2
in³
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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: Find the radius of the base

The diameter of the base is given as \( 14.3 \) in. The radius \( r \) is half of the diameter, so \( r=\frac{14.3}{2}=7.15 \) in.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know that \( h = 18.8 \) in and \( r=7.15 \) in. Substituting these values into the formula \( V=\frac{1}{3}\pi r^2 h \), we get:

$$ V=\frac{1}{3}\times\pi\times(7.15)^2\times18.8 $$

Step4: Calculate the value

First, calculate \( (7.15)^2=7.15\times7.15 = 51.1225 \)
Then, multiply by \( 18.8 \): \( 51.1225\times18.8 = 51.1225\times(18 + 0.8)=51.1225\times18+51.1225\times0.8=920.205+40.898 = 961.103 \)
Then, multiply by \( \frac{1}{3}\pi \): \( V=\frac{1}{3}\times\pi\times961.103\approx\frac{1}{3}\times3.14159\times961.103 \)
\( \frac{3.14159\times961.103}{3}=\frac{3019.03}{3}\approx1006.34 \) (rounded to the nearest tenth)

Answer:

\( 1006.3 \)