Question

which equation represents the volume of the cone shown below, in cubic centimeters?
options:

• $v = 80 × 150 × π$
• $v = \frac{1}{3} × π × 80^2 × 150$
• $v = \frac{1}{3} × π × 80^2 × 170$
• $v = 80 × 150 × 170 × π$

Explanation:

Step1: Recall cone volume formula

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

Step2: Identify values from the diagram

From the cone, the base radius $r = 80$ cm, and the perpendicular height $h = 150$ cm (the slant height of 170 cm is not used for volume).

Step3: Substitute values into the formula

Substitute $r=80$ and $h=150$ into the volume formula:
$V = \frac{1}{3} \times \pi \times 80^2 \times 150$

Answer:

$\boldsymbol{V = \frac{1}{3} \times \pi \times 80^2 \times 150}$ (the second option)