Question

find the height of a cone with a diameter of 12 m who volume is 264 m³. use 3.14 for π, and round your answer to the nearest meter. 2 of 5 questio 42 m 6 m 2 m 7 m

Explanation:

Step1: Find the radius

The diameter \(d = 12\) m. The radius \(r=\frac{d}{2}=\frac{12}{2}=6\) m.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). We know \(V = 264\) \(m^{3}\), \(\pi=3.14\), and \(r = 6\) m. Substitute these values into the formula:
\(264=\frac{1}{3}\times3.14\times6^{2}\times h\)
First, calculate \(6^{2}=36\). Then \(\frac{1}{3}\times3.14\times36 = 3.14\times12=37.68\).
The equation becomes \(264 = 37.68h\).

Step3: Solve for \(h\)

\(h=\frac{264}{37.68}\approx7\)

Answer:

7 m