Question

Faye ordered a case of sugar cones for her ice cream shop. One cone is shown.

Which measurement is closest to the volume of the ice cream cone?


At the top of the cone is 6 cm and on the side is 16 cm

Answer 1

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

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

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

From the given dimensions, it is stated that the top (diameter) of the cone is 6 cm, which means the radius \( r \) is half of that:

\[
r = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm}
\]

The height \( h \) of the cone is given as 16 cm.

Now we can substitute these values into the volume formula:

\[
V = \frac{1}{3} \pi (3 \, \text{cm})^2 (16 \, \text{cm})
\]

Calculating \( r^2 \):

\[
r^2 = 3^2 = 9 \, \text{cm}^2
\]

Now plugging in the values:

\[
V = \frac{1}{3} \pi (9 \, \text{cm}^2)(16 \, \text{cm}) = \frac{1}{3} \pi (144 \, \text{cm}^3)
\]

Now compute:

\[
V = \frac{144 \pi}{3} \, \text{cm}^3 = 48 \pi \, \text{cm}^3
\]

To get a numerical value, we can use \( \pi \approx 3.14 \):

\[
V \approx 48 \times 3.14 \, \text{cm}^3 \approx 150.72 \, \text{cm}^3
\]

So, the volume of the ice cream cone is approximately **150.72 cm³**.