To find the volume of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] represents the volume of the cylinder
- [tex]\( r \)[/tex] represents the radius of the base of the cylinder
- [tex]\( h \)[/tex] represents the height of the cylinder
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159
Given that the radius [tex]\( r \)[/tex] is 8 feet and the height [tex]\( h \)[/tex] is 7 feet, we can substitute these values into the formula to get:
[tex]\[ V = \pi (8^2) \times 7 \][/tex]
[tex]\[ V = \pi \times 64 \times 7 \][/tex]
We calculate the squared radius and multiply by the height:
[tex]\[ V = 3.14159 \times 64 \times 7 \][/tex]
[tex]\[ V ≈ 3.14159 \times 448 \][/tex]
[tex]\[ V ≈ 1407.95712 \][/tex]
Now, we want to round the volume to the nearest tenth:
[tex]\[ V ≈ 1408.0 \][/tex]
So, the volume of the cylinder, rounded to the nearest tenth, is approximately 1408.0 cubic feet.
