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

A. 100.5 cm3
B. 150.8 cm 3
C. 603.2 cm 3
D. 452.4 cm 3

Answer 1

To find the volume of a cone, we use the formula:

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

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

From the problem, you mentioned the "top of the cone is 6 cm", which likely refers to the diameter, so:

1. **Determine the radius:**
- Diameter = 6 cm, therefore, the radius \( r = \frac{6}{2} = 3 \) cm.

2. **Determine the height:**
- The height \( h \) is given as the length of the side (slant height) which is 16 cm. However, we need the vertical height of the cone, not the slant height. We can find the vertical height using the Pythagorean theorem because the radius (3 cm) and the height of the cone form a right triangle with the slant height (16 cm).
- Let \( h \) be the vertical height. We have:
\[
h^2 + r^2 = \text{slant height}^2
\]
\[
h^2 + 3^2 = 16^2
\]
\[
h^2 + 9 = 256
\]
\[
h^2 = 256 - 9 = 247
\]
\[
h = \sqrt{247} \approx 15.7 \text{ cm}
\]

Now we have the radius \( r = 3 \) cm and height \( h \approx 15.7 \) cm.

3. **Substituting into the volume formula:**
\[
V = \frac{1}{3} \pi (3)^2 (15.7)
\]
\[
V = \frac{1}{3} \pi (9)(15.7)
\]
\[
V = \frac{1}{3} \pi (141.3)
\]
\[
V \approx \frac{141.3}{3} \pi \approx 47.1 \pi \approx 147.5 \text{ cm}^3
\]

Thus, the volume of the cone is closest to **B. 150.8 cm³**.