Question

a cone has a height of 13 inches and a radius of 9 inches. what is its volume? round your answer to the nearest hundredth. cubic inches submit

Explanation:

Step1: 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 and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given that \( r = 9 \) inches and \( h = 13 \) inches. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\pi(9)^2(13) \)
First, calculate \( 9^2 = 81 \). Then the expression becomes:
\( V=\frac{1}{3}\pi\times81\times13 \)
\( \frac{1}{3}\times81 = 27 \), so now we have:
\( V = 27\times13\times\pi \)
\( 27\times13 = 351 \), so:
\( V = 351\pi \)

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\( V\approx351\times3.14159 \)
\( 351\times3.14159 = 351\times3 + 351\times0.14159 = 1053+49.69809 = 1102.69809 \)

Step4: Round to the nearest hundredth

Rounding \( 1102.69809 \) to the nearest hundredth gives \( 1102.70 \) (since the thousandth place is 8, which is greater than 5, we round up the hundredth place).

Answer:

\( 1102.70 \)