Question

figure is not drawn to scale.
a) select the appropriate formula to determine volume of a cone.
$bh$ $\frac{1}{3}\pi r^2 h$ $\frac{4}{3}\pi r^3$ $\pi r^2 h$ $lwh$ $\frac{1}{3}bh$
part 2 of 3
b) identify the variables.
$r = \square$ ft $h = \square$ un
question help: video

Explanation:

Part (a)

Step1: Recall Cone Volume Formula

The volume \( V \) of a cone is given by the formula that accounts for one - third of the volume of a cylinder (since a cone with the same base and height as a cylinder has one - third the volume of the cylinder). The volume of a cylinder is \( \pi r^{2}H \), so the volume of a cone is \( \frac{1}{3}\pi r^{2}H \).

• \( BH \) is a formula for the area of a parallelogram (base times height) or other shapes, not for the volume of a cone.
• \( \frac{4}{3}\pi r^{3} \) is the formula for the volume of a sphere.
• \( \pi r^{2}H \) is the formula for the volume of a cylinder.
• \( LWH \) is the formula for the volume of a rectangular prism (length times width times height).
• \( \frac{1}{3}BH \) is the formula for the volume of a pyramid (where \( B \) is the area of the base and \( H \) is the height), not a cone.

Step1: Identify the radius (\(r\))

From the diagram, the radius of the base of the cone is given as \( 9\) ft. So \( r = 9\) ft.

Step2: Identify the height (\(H\))

From the diagram, the height of the cone is given as \( 27\) ft. So \( H=27\) ft.

Answer:

\(\boldsymbol{\frac{1}{3}\pi r^{2}H}\)

Part (b)