Question

gabby is making a tree sculpture out of modeling clay in her art class. the trunk of the tree will be a cylinder, and the top will be a cone. the dimensions of the tree sculpture are shown below. what percent of the trees total volume is made up by the trunk? round your answer to the nearest percent. % submit

Explanation:

Step1: Calculate the volume of the cylinder (trunk)

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). The radius \(r = 1.6\div2=0.8\) cm and height \(h = 4\) cm.

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Step2: Calculate the volume of the cone

The formula for the volume of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). The radius \(r = 3.5\) cm and height \(h = 9\) cm.

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Step3: Calculate the total volume

\(V_{total}=V_{cylinder}+V_{cone}=2.56\pi + 36.75\pi=39.31\pi\space\text{cm}^{3}\)

Step4: Calculate the percentage of the trunk's volume

The percentage \(P=\frac{V_{cylinder}}{V_{total}}\times 100=\frac{2.56\pi}{39.31\pi}\times 100\)
Since \(\pi\) cancels out, \(P=\frac{2.56}{39.31}\times 100\approx 6.51\approx7\)

Answer:

\(7\)