Question

as office manager, rahn wants to ensure he is getting the best deal on paper cups. the office currently uses the cups shown. what is the volume of the cup to the nearest hundredth?

Explanation:

Step1: Identify the radius

The diameter of the cone - shaped cup is given as $d = 2.75$ inches. The radius $r=\frac{d}{2}=\frac{2.75}{2}=1.375$ inches, and the height $h = 4$ inches.

Step2: Use the volume formula for a cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 1.375$ inches and $h = 4$ inches into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(1.375)^{2}\times4\\ &=\frac{1}{3}\times\pi\times1.890625\times 4\\ &=\frac{7.5625\pi}{3}\\ &\approx\frac{7.5625\times3.14159}{3}\\ &=\frac{23.729}{3}\\ &\approx7.91 \end{align*}$$

\]

Answer:

$7.91$ cubic - inches