Question

a frustum is formed when a plane parallel to a cones base cuts off the upper portion as shown. which expression represents the volume, in cubic units, of the frustum? \\(\frac{1}{3}\pi(7.5^2)(11) - \frac{1}{3}\pi(3.5^2)(8)\\) \\(\frac{1}{3}\pi(7.5^2)(11) + \frac{1}{3}\pi(3.5^2)(8)\\) \\(\frac{1}{3}\pi(7.5^2)(19) - \frac{1}{3}\pi(3.5^2)(8)\\) \\(\frac{1}{3}\pi(7.5^2)(19) + \frac{1}{3}\pi(3.5^2)(8)\\)

Explanation:

Step1: Recall frustum volume logic

The volume of a frustum is the volume of the large original cone minus the volume of the small cut-off cone.

Step2: Identify large cone dimensions

The large cone has height $8 + 11 = 19$ and radius $7.5$. Its volume is $\frac{1}{3}\pi(7.5^2)(19)$.

Step3: Identify small cone dimensions

The small cut-off cone has height $8$ and radius $3.5$. Its volume is $\frac{1}{3}\pi(3.5^2)(8)$.

Step4: Set up frustum volume formula

Subtract the small cone volume from the large cone volume.

Answer:

$\boldsymbol{\frac{1}{3}\pi(7.5^2)(19) - \frac{1}{3}\pi(3.5^2)(8)}$ (third option)