Question

the volume of this cone is 1,186.92 cubic meters. what is the height of this cone? round your answer to the nearest hundredth. 9 m h ≈ meters

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 know \( V = 1186.92 \) cubic meters and \( r = 9 \) meters. We need to solve for \( h \).

Step2: Rearrange the formula for \( h \)

Starting with \( V = \frac{1}{3}\pi r^2 h \), multiply both sides by 3: \( 3V = \pi r^2 h \). Then divide both sides by \( \pi r^2 \): \( h = \frac{3V}{\pi r^2} \).

Step3: Substitute the known values

Substitute \( V = 1186.92 \), \( r = 9 \), and \( \pi \approx 3.14 \) into the formula:
\( h = \frac{3 \times 1186.92}{3.14 \times 9^2} \)

Step4: Calculate the denominator

First, calculate \( 9^2 = 81 \), then \( 3.14 \times 81 = 254.34 \).

Step5: Calculate the numerator

Calculate \( 3 \times 1186.92 = 3560.76 \).

Step6: Divide numerator by denominator

\( h = \frac{3560.76}{254.34} = 14 \).

Answer:

14.00