Question

find the volume of a right circular cone that has a height of 7.8 m and a base with a diameter of 2.3 m. round your answer to the nearest tenth of a cubic meter.

Explanation:

Step1: Find the radius of the base

The diameter of the base is 2.3 m, so the radius \( r \) is half of the diameter.
\( r=\frac{2.3}{2}=1.15\space m \)

Step2: Recall the formula for the volume of a cone

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

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know that \( r = 1.15\space m \) and \( h=7.8\space m \). Substituting these values into the formula:
\( V=\frac{1}{3}\times\pi\times(1.15)^{2}\times7.8 \)

First, calculate \( (1.15)^{2}=1.3225 \)

Then, \( \frac{1}{3}\times\pi\times1.3225\times7.8=\frac{1}{3}\times\pi\times10.3155 \)

\( \frac{10.3155}{3}\times\pi = 3.4385\times\pi \)

Using \( \pi\approx3.1416 \), we get \( 3.4385\times3.1416\approx10.8\space m^{3} \) (rounded to the nearest tenth)

Answer:

\( 10.8 \) cubic meters