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? 1/3pi(7.5^2)(11) - 1/3pi(3.5^2)(8) 1/3pi(7.5^2)(11) + 1/3pi(3.5^2)(8) 1/3pi(7.5^2)(19) - 1/3pi(3.5^2)(8) 1/3pi(7.5^2)(19) + 1/3pi(3.5^2)(8)

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$.

Step2: Understand volume of frustum

The volume of the frustum is the volume of the large - cone (with radius $r_1 = 7.5$ and height $h_1=11 + 8=19$) minus the volume of the small - cone (with radius $r_2 = 3.5$ and height $h_2 = 8$).
The volume of the large cone is $V_1=\frac{1}{3}\pi(7.5^{2})(19)$ and the volume of the small cone is $V_2=\frac{1}{3}\pi(3.5^{2})(8)$.
So the volume of the frustum is $V = \frac{1}{3}\pi(7.5^{2})(19)-\frac{1}{3}\pi(3.5^{2})(8)$.

Answer:

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