Question

find the missing dimension of the cone. round your answer to the nearest tenth. volume = 225 cm³ 16

Explanation:

Step1: Find the radius

The diameter is \(10\) cm, so the radius \(r=\frac{10}{2} = 5\) cm.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). We know \(V = 225\) \(cm^{3}\) and \(r = 5\) cm. Substitute these values into the formula:

$$225=\frac{1}{3}\pi(5)^{2}h$$

$$225=\frac{25\pi}{3}h$$

Step3: Solve for \(h\)

First, multiply both sides by \(3\):

$$225\times3 = 25\pi h$$

$$675=25\pi h$$

Then divide both sides by \(25\pi\):

$$h=\frac{675}{25\pi}$$

$$h=\frac{27}{\pi}$$

Using \(\pi\approx3.14\), we have \(h=\frac{27}{3.14}\approx8.6\)

Answer:

\(8.6\)