Question

a cone has a volume of 3183.96 cubic inches and a radius of 13 inches. what is its height? round your answer to the nearest hundredth. h ≈ \boxed{} inches submit

Explanation:

Step1: Recall cone volume formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We need to solve for \( h \), so rearrange the formula: \( h=\frac{3V}{\pi r^2} \).

Step2: Substitute given values

Given \( V = 3183.96 \) cubic inches and \( r = 13 \) inches. Substitute into the formula: \( h=\frac{3\times3183.96}{\pi\times13^2} \).

Step3: Calculate denominator

First, calculate \( 13^2 = 169 \), then \( \pi\times169\approx3.1416\times169 = 530.92944 \).

Step4: Calculate numerator

Calculate \( 3\times3183.96 = 9551.88 \).

Step5: Divide numerator by denominator

Now, divide \( 9551.88 \) by \( 530.92944 \): \( h\approx\frac{9551.88}{530.92944}\approx17.99 \) (rounded to the nearest hundredth).

Answer:

\( 17.99 \)