Given:
The height of the cylinder = 12 in
The diameter of the base of the cylinder = 8 in.
To find:
The volume of the cylinder.
Solution:
The diameter of the base of the cylinder is 8 in. The radius is half of its diameter. So,
[tex]r=\dfrac{8}{2}[/tex]
[tex]r=4[/tex]
So, the radius of the base of the cylinder is 4 in.
The height of the cylinder, h = 12 in.
Base area of the cylinder is:
[tex]B=\pi r^2[/tex]
Where, B is the base area and r is the radius.
[tex]B=\pi (4)^2[/tex]
[tex]B=16\pi [/tex]
So, the base area is [tex]16\pi [/tex] square inches.
The volume of the cylinder is:
[tex]V=\pi r^2h[/tex]
[tex]V=Bh[/tex]
Where, r is radius, h is height, B is base area.
Putting [tex]B=16\pi [/tex] and [tex]h=12[/tex], we get
[tex]V=(16\pi )12[/tex]
[tex]V=192\pi [/tex]
So, the volume is [tex]192\pi [/tex] cubic inches.
Therefore, [tex]r=4\text{ in}, h=12\text{ in},B=16\pi \text{ in}^2,V=192\pi \text{ in}^3[/tex].
