Question

A cylindrial hole is cut through the cylinder below.

below. The larger Cylinder has a diameter of 14 mm and a height of 25 mm. If the diameter of the hole is 10 mm, find the volume of the solid.

Answer 1

V=1884 Cubic mm

Explanation:

We know that the volume of the Sphere is given by the formula

`V= \pi r^2h`

Where r is the radius and h is the height of the cylinder

We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.

`V=V_1-V_2`

`V=\pi r_1^2 * h-\pi r_2^2 * h`

`V=\pi * h * (r_1^2-r_2^2)`

Where

`V_1` is the the volume of solid cylinder with radius
`r_1` and height h

`V_2` is the volume of the cylinder being carved out with radius
`r_2` and height h

where

`r_1 = 7` mm ( Half of the bigger diameter )

`r_2 = 5` mm ( Half of the inner diameter )

`h=25` mm

Putting these values in the formula for V we get

`V=\pi * 25* (7^2-5^2)`

`V=3.14 * 25 *(49-25)`

`V=3.14 * 25 * 24`

`V= 1884`