To find the volume of a cylinder, you use the formula for the volume of a cylinder, which is:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the base radius of the cylinder, and [tex]\( h \)[/tex] is the height of the cylinder.
In this problem:
- The height [tex]\( h \)[/tex] is 11 cm.
- The base radius [tex]\( r \)[/tex] is 9 cm.
1. First, calculate the area of the base of the cylinder. The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex]:
[tex]\[ A = \pi \times r^2 \][/tex]
[tex]\[ A = \pi \times 9^2 \][/tex]
[tex]\[ A = \pi \times 81 \][/tex]
2. Next, multiply the area of the base by the height [tex]\( h \)[/tex]:
[tex]\[ V = A \times h \][/tex]
[tex]\[ V = (\pi \times 81) \times 11 \][/tex]
Now, substitute the value of [tex]\(\pi \)[/tex] (approximately 3.14159) into the equation to find:
[tex]\[ V = (3.14159 \times 81) \times 11 \][/tex]
[tex]\[ V \approx (254.469) \times 11 \][/tex]
[tex]\[ V \approx 2799.1590543485054 \][/tex]
Finally, rounding to the nearest tenths place:
[tex]\[ V \approx 2799.2 \][/tex]
Therefore, the volume of the cylinder to the nearest tenths place is 2799.2 cubic cm.
