Question

The plastic cylinder has a diameter of 2 cm. There is a rectangular 0.6 cm square prism through the middle of the cylinder, extending from the top to the bottom. The height of the cylinder is 6 cm. Find the volume of the cylinder without the prism.

Answer 1

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.

Explanation:

The volume of the cylinder without the prism can be defined as the volume of the entire cylinder (
`V_(cy)`), measured in cubic centimeters, minus the volume of the prism (
`V_(pr)`), measured in cubic centimeters. That is:

`V = V_(cy)-V_(pr )` (1)

`V = (\pi)/(4)\cdot D^(2)\cdot h - l^(2)\cdot h`

`V = \left((\pi)/(4)\cdot D^(2)-l^(2) \right)\cdot h` (2)

Where:

`D` - Diameter of the cylinder, measured in centimeters.

`l` - Side of the square prism, measured in centimeters.

`h` - Height of the square prism, measured in centimeters.

If we know that
`D = 2\,cm`,
`l = 0.6\,cm` and
`h = 6\,cm`, then the volume of the cylinder without the prism is:

`V = \left[(\pi)/(4)\cdot (2\,cm)^(2)-(0.6\,cm)^(2) \right]\cdot (6\,cm)`

`V \approx 16.690\,cm^(3)`

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.