Question

A new restaurant specializes in making pizza cones. A large slice of pizza is made into a cone shape and then filled with cheese, meat, or vegetables.
The cone formed by the slice of pizza measures 5 inches tall and has a diameter of 3 inches.
How many cubic inches of fillings can the cone hold?
Use 3.14 for pi.
Enter your answer in the box as a decimal rounded to the nearest tenth.

In^3

Answer 1

To find the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius of the base of the cone, and \( h \) is the height of the cone.

First, we need to find the radius. The diameter of the cone is given as 3 inches, so the radius \( r \) is half of that:

\[
r = \frac{3}{2} = 1.5 \text{ inches}
\]

The height \( h \) of the cone is given as 5 inches.

Now, we can plug in these values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 5
\]

Calculate \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now substitute back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 2.25 \times 5
\]

Calculate \( 3.14 \times 2.25 \):

\[
3.14 \times 2.25 = 7.065
\]

Now multiply by 5:

\[
7.065 \times 5 = 35.325
\]

Now we multiply by \(\frac{1}{3}\):

\[
V = \frac{35.325}{3} = 11.775
\]

Finally, rounded to the nearest tenth, the volume is:

\[
\boxed{11.8} \text{ cubic inches}
\]