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 pie . use whole numbers or decimals for any numbers in the expression. )

Respuesta :

The volume of a cone can be calculated with the following formula:

[tex]V=\frac{\pi r^2h}{3}[/tex]

Where "r" is the radius and "h" is the height of the cone.

By definition, the radius is half the diameter. Then, in this case:

[tex]\begin{gathered} r=\frac{15in}{2} \\ \\ r=7.5in \end{gathered}[/tex]

Knowing that the height of the waffle ice cream cone is:

[tex]h=25in[/tex]

You can substitute values into the formula and then evaluate, in order to find the volume of the waffle ice cream cone. Then:

[tex]\begin{gathered} V=\frac{\pi(7.5in)^2(25in)}{3} \\ \\ V=^{}\frac{1875}{4}\pi in^3 \\ \\ V=468.75\pi in^3 \end{gathered}[/tex]

The answer is:

[tex]V=468.75\pi in^3[/tex]