Question

study next figure. what is the volume of the figure if cb = 3.5 inches and ab = 12 inches? use 3.14 for π. do not round off any value during the computation. round your final answer to the nearest tenth.

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Here, \(r = CB = 3.5\) inches and \(h=AB = 12\) inches.

Step2: Substitute the values into the formula

Substitute \(r = 3.5\), \(h = 12\), and \(\pi=3.14\) into \(V=\frac{1}{3}\pi r^{2}h\).
First, calculate \(r^{2}\): \(r^{2}=(3.5)^{2}=3.5\times3.5 = 12.25\).
Then, calculate \(\pi r^{2}h\): \(3.14\times12.25\times12\).
\(3.14\times12.25 = 3.14\times(12 + 0.25)=3.14\times12+3.14\times0.25=37.68+0.785 = 38.465\).
\(38.465\times12=461.58\).
Finally, calculate \(\frac{1}{3}\pi r^{2}h\): \(V=\frac{1}{3}\times461.58\).
\(V = 153.86\).

Answer:

\(153.9\) cubic inches.