Volume of Cones Practice

Question

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Question
A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π
.(1 point)
cubic feet

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

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

1. Find the radius: The diameter of the cone is 12 feet, so the radius \( r \) is:

\[ r = \frac{d}{2} = \frac{12}{2} = 6 \text{ feet} \]

2. Use the height: The height \( h \) is given as 15 feet.

3. Plug the values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15 \]

4. Calculate \( (6)^2 \):

\[ (6)^2 = 36 \]

5. Substitute back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \]

6. Multiply:

\[ 36 \times 15 = 540 \]

7. Now calculate:

\[ V = \frac{1}{3} \times 3.14 \times 540 \]

8. Multiply \( 3.14 \times 540 \):

\[ 3.14 \times 540 = 1695.6 \]

9. Divide by 3:

\[ V = \frac{1695.6}{3} = 565.2 \]

So, the volume of water the tank can hold is approximately

\[ \boxed{565.2} \text{ cubic feet}. \]