Question

How much bigger is a the volume of a cone with radius of
12
12 feet and a height of
21
21 feet than a cone with radius of
6
6 feet and a height of
21
21 feet? Use 3.14 for π. Click Here for Help Video



The difference in the volumes of the cones is
cubic feet.

Answer 1

To find the difference in volume between the two cones, we first need to calculate the volume of each cone using 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, and \( h \) is the height.

**For the first cone (radius = 12 feet, height = 21 feet):**

\[
V_1 = \frac{1}{3} \pi (12)^2 (21)
\]

Calculating this step by step:

1. Calculate \( (12)^2 = 144 \).
2. Then, calculate \( V_1 = \frac{1}{3} \times 3.14 \times 144 \times 21 \).

Now, calculate \( 144 \times 21 \):

\[
144 \times 21 = 3024
\]

Now substitute back into the volume formula:

\[
V_1 = \frac{1}{3} \times 3.14 \times 3024
\]

Calculate \( 3.14 \times 3024 \):

\[
3.14 \times 3024 \approx 9485.76
\]

Now, finally calculate \( V_1 \):

\[
V_1 = \frac{1}{3} \times 9485.76 \approx 3161.92 \text{ cubic feet}
\]

**For the second cone (radius = 6 feet, height = 21 feet):**

\[
V_2 = \frac{1}{3} \pi (6)^2 (21)
\]

Following similar steps:

1. Calculate \( (6)^2 = 36 \).
2. Calculate \( V_2 = \frac{1}{3} \times 3.14 \times 36 \times 21 \).

Now calculate \( 36 \times 21 \):

\[
36 \times 21 = 756
\]

Now substitute into the volume formula:

\[
V_2 = \frac{1}{3} \times 3.14 \times 756
\]

Calculate \( 3.14 \times 756 \):

\[
3.14 \times 756 \approx 2377.44
\]

Now calculate \( V_2 \):

\[
V_2 = \frac{1}{3} \times 2377.44 \approx 792.48 \text{ cubic feet}
\]

**Now, calculate the difference in volumes:**

\[
\text{Difference} = V_1 - V_2 = 3161.92 - 792.48 \approx 2369.44 \text{ cubic feet}
\]

Thus, the difference in the volumes of the cones is approximately:

\[
\boxed{2369.44} \text{ cubic feet}
\]