Question

1. a cone has a height of 11 meters and a radius of 4 meters. what is the volume of the cone, in cubic meters, rounded to the nearest hundredth? cubic meters

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume \( V \) of a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values into the formula

Given \( r = 4\) meters and \( h=11\) meters. Substitute into the formula: \( V=\frac{1}{3}\times\pi\times(4)^{2}\times11\).
First, calculate \( (4)^{2}=16 \). Then the expression becomes \( V=\frac{1}{3}\times\pi\times16\times11=\frac{176\pi}{3}\).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V=\frac{176\times3.14159}{3}\).
\( 176\times3.14159 = 552.92984 \). Then \( V=\frac{552.92984}{3}=184.3099467\).
Rounding to the nearest hundredth (two - decimal places), we get \( V\approx184.31\).

Answer:

\( 184.31\)