Question

find the exact volume of a waffle ice cream cone with a 15-in. diameter and a height of 25 inches. the exact volume of the waffle ice cream cone is (type an exact answer in terms of π. use whole numbers or decimals for any numbers in the expression.)

Explanation:

Step1: Find the radius

The diameter is 15 in, so the radius \( r = \frac{15}{2} = 7.5 \) in.

Step2: Use the volume formula for a cone

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( h = 25 \) in. Substitute \( r = 7.5 \) and \( h = 25 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi(7.5)^2(25)\\ &=\frac{1}{3}\pi(56.25)(25)\\ &=\frac{1}{3}\pi(1406.25)\\ & = 468.75\pi \end{align*}$$

\]

Answer:

\( 468.75\pi \) cubic inches