What is the volume of a cylinder with a diameter of 8' and height of 15'?

To determine the volume of a cylinder, the formula used is:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius of the cylinder, and ( h ) is the height.

1. First, calculate the radius. The diameter of the cylinder is given as 8 feet. The radius is half of the diameter, so:

[ r = \frac{8'}{2} = 4' ]

2. Next, substitute the radius and the height into the volume formula. The height, given, is 15 feet. Plugging the values into the formula yields:

[ V = \pi (4')^2 (15') ]

3. Calculate ( (4')^2 ):

[ (4')^2 = 16 \text{ ft}^2 ]

4. Now plug this value back into the equation:

[ V = \pi (16 \text{ ft}^2) (15') ]

5. Multiply 16 by 15:

[ 16 \times 15 = 240 \text{ ft}^3 ]

6. Finally, multiply by ( \pi ) (approximately