Question

an office uses paper drinking cups in the shape of a cone, with dimensions as shown. to the nearest tenth of a cubic inch, what is the volume of each drinking cup?

Explanation:

Step1: Recall volume formula for cone

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

Step2: Find the radius

The diameter $d = 2\frac{3}{4}=\frac{11}{4}$ inches. The radius $r=\frac{d}{2}=\frac{11}{8}$ inches, and the height $h = 4$ inches.

Step3: Substitute values into formula

$V=\frac{1}{3}\pi(\frac{11}{8})^{2}\times4=\frac{1}{3}\pi\times\frac{121}{64}\times4=\frac{121\pi}{48}$

Step4: Calculate the value

$V=\frac{121\pi}{48}\approx\frac{121\times3.14}{48}\approx\frac{380.94}{48}\approx7.9$ cubic - inches

Answer:

$7.9$ cubic inches