Question

multiple choice
question 6
find the volume of the cone to the nearest tenth.
volume of a cone = \\( \frac { 1 } { 3 } \pi r ^ { 2 } h \\)
a cone

Explanation:

Step1: Substitute the values into the formula

Given \(r = 3\) yards and \(h=4\) yards. The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 3\) and \(h = 4\) into the formula: \(V=\frac{1}{3}\times\pi\times(3)^{2}\times4\).

Step2: Simplify the expression

First, calculate \((3)^{2}=9\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times9\times4\). Since \(\frac{1}{3}\times9 = 3\), the formula simplifies to \(V = 3\times\pi\times4\).

Step3: Calculate the final value

\(3\times4=12\), so \(V = 12\pi\). Using \(\pi\approx3.14\), we get \(V\approx12\times3.14=37.68\). Rounding \(37.68\) to the nearest tenth gives \(V\approx37.7\) cubic yards.

Answer:

\(37.7\) cubic yards