Question

an error occurs in the volume calculation of the cone below. recalculate the volume correctly.
$v = \frac{1}{3}bh = \frac{1}{3}(\pi)(6)^2(8) = 96\pi\\ \text{m}^3$
the volume of the cone is \\(\boxed{}\\ \text{m}^2\\).

Explanation:

Step1: Identify radius and height

From the diagram, the diameter of the base is 6 m, so radius \( r = \frac{6}{2} = 3 \) m. The height \( h = 8 \) m.

Step2: Use cone volume formula

The formula for the volume of a cone is \( V = \frac{1}{3}\pi r^2 h \). Substitute \( r = 3 \) and \( h = 8 \):
\( V = \frac{1}{3}\pi (3)^2 (8) \)

Step3: Calculate the volume

First, \( (3)^2 = 9 \). Then, \( \frac{1}{3} \times 9 = 3 \). Then, \( 3 \times 8 = 24 \). So \( V = 24\pi \) cubic meters.

Answer:

\( 24\pi \)