Question

question
the volume of a tree stump can be modeled by considering it as a right cylinder. lauren
measures its height as 0.8 ft and its volume as 26146 cubic inches. find the stumps diameter
in inches. round your answer to the nearest tenth if necessary.
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Convert height to inches

Since \(1\) foot \( = 12\) inches, the height \(h\) of the cylinder (tree - stump) is \(h=0.8\times12 = 9.6\) inches.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). We know \(V = 26146\) cubic inches and \(h = 9.6\) inches. First, solve for \(r^{2}\):

$$r^{2}=\frac{V}{\pi h}$$

Substitute \(V = 26146\) and \(h = 9.6\):

$$r^{2}=\frac{26146}{\pi\times9.6}$$

$$r^{2}=\frac{26146}{30.15928947}$$

$$r^{2}\approx867.0$$

Step3: Find the radius

Take the square - root of \(r^{2}\): \(r=\sqrt{867.0}\approx29.44\) inches.

Step4: Find the diameter

Since \(d = 2r\), \(d=2\times29.44 = 58.9\) inches.

Answer:

\(58.9\) inches