Question

Alex makes a cone out of paper with a height thats twice the length of the diameter. The diameter of the cone is 6 cm. Find the volume of the paper cone

Answer 1

To find the volume of the cone, we first need to determine its radius and height.

1. **Diameter of the cone** = 6 cm
Therefore, the radius \( r \) is half of the diameter:
\[
r = \frac{6 \text{ cm}}{2} = 3 \text{ cm}
\]

2. **Height of the cone**: The problem states that the height is twice the length of the diameter. The diameter is 6 cm, so:
\[
h = 2 \times 6 \text{ cm} = 12 \text{ cm}
\]

3. **Volume of the cone formula**: The volume \( V \) of a cone is given by:
\[
V = \frac{1}{3} \pi r^2 h
\]

4. **Substituting the values of \( r \) and \( h \)**:
\[
V = \frac{1}{3} \pi (3 \text{ cm})^2 (12 \text{ cm})
\]
\[
= \frac{1}{3} \pi (9 \text{ cm}^2) (12 \text{ cm})
\]
\[
= \frac{1}{3} \pi (108 \text{ cm}^3)
\]
\[
= 36 \pi \text{ cm}^3
\]

5. **Calculating the approximate volume**:
Using \( \pi \approx 3.14 \):
\[
V \approx 36 \times 3.14 \text{ cm}^3 \approx 113.04 \text{ cm}^3
\]

Thus, the volume of the paper cone is \( 36 \pi \text{ cm}^3 \) or approximately \( 113.04 \text{ cm}^3 \).