Question

a cone has a diameter of 3 inches. the cone holds 12 cubic inches of water. to the nearest inch, what is the height of the cone?
o a. 1
o b. 4
o c. 5
o d. 8

Explanation:

Step1: Find the radius

The diameter \(d = 3\) inches. The radius \(r=\frac{d}{2}=\frac{3}{2}=1.5\) inches.

Step2: Use the volume formula of a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). We know \(V = 12\) cubic inches and \(r = 1.5\) inches. Substitute these values into the formula:
\(12=\frac{1}{3}\times\pi\times(1.5)^{2}\times h\)
First, calculate \((1.5)^{2}=2.25\). Then the equation becomes \(12=\frac{1}{3}\times\pi\times2.25\times h\).
\(\frac{1}{3}\times2.25 = 0.75\), so \(12 = 0.75\pi h\).
Solve for \(h\): \(h=\frac{12}{0.75\pi}\).
Since \(\pi\approx3.14\), \(h=\frac{12}{0.75\times3.14}=\frac{12}{2.355}\approx5.1\)

Answer:

C. 5