To find the volume of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the cylinder.
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14.
- [tex]\( r \)[/tex] is the radius of the base of the cylinder.
- [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- Radius ([tex]\( r \)[/tex]) = 13 feet
- Height ([tex]\( h \)[/tex]) = 14 feet
- [tex]\( \pi \approx 3.14 \)[/tex]
Let's calculate the volume step-by-step:
1. First, calculate the area of the base (which is a circle) using the formula [tex]\( \pi r^2 \)[/tex].
[tex]\[ \pi r^2 = 3.14 \times (13)^2 \][/tex]
2. Calculate [tex]\( (13)^2 \)[/tex]:
[tex]\[ (13)^2 = 169 \][/tex]
3. Now, multiply by [tex]\( \pi \)[/tex] (approximately 3.14):
[tex]\[ 3.14 \times 169 = 530.66 \][/tex]
4. Now that we have the area of the base, we multiply this by the height of the cylinder to get the volume:
[tex]\[ V = \text{Area of base} \times \text{Height} = 530.66 \times 14 \][/tex]
5. Finally, perform the multiplication:
[tex]\[ 530.66 \times 14 = 7429.24 \][/tex]
Thus, the volume of the cylinder, rounded to the nearest hundredth, is:
[tex]\[ V \approx 7429.24 \ \text{cubic feet} \][/tex]
So, the volume of the cylinder is [tex]\( 7429.24 \ \text{cubic feet} \)[/tex].
