Question

a cone has a volume of 1526.04 cubic meters and a radius of 9 meters. what is its height? round your answer to the nearest hundredth. h ≈ \boxed{} meters 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 \( V = 1526.04 \) cubic meters and \( r = 9 \) meters. Substitute into the formula: \( h = \frac{3 \times 1526.04}{\pi \times 9^2} \).

Step3: Calculate denominator

First, calculate \( 9^2 = 81 \), then \( \pi \times 81 \approx 3.1416 \times 81 \approx 254.4696 \).

Step4: Calculate numerator

Calculate \( 3 \times 1526.04 = 4578.12 \).

Step5: Divide numerator by denominator

Now, \( h = \frac{4578.12}{254.4696} \approx 18.0 \) (wait, let's do the division more accurately: \( 4578.12 \div 254.4696 \approx 18.0 \)? Wait, no, let's check again. Wait, \( \pi \) is approximately 3.14, so \( 3.14 \times 81 = 254.34 \). Then \( 4578.12 \div 254.34 = 18.0 \)? Wait, 254.34 * 18 = 4578.12. Oh, right! So \( h \approx 18.00 \) when rounded to the nearest hundredth.

Answer:

\( 18.00 \)