Question

A kaleidoscope has been created by cutting a regular hexagonal hole with side length 2 cm through a cylinder. Find the volume of this kaleidoscope.

Answer 1

The volume of the kaleidoscope (hollow cylinder) is 613.33 in.³

Explanation:

Here we have;

The equation for the volume of a cylinder given as follows;

Volume of cylinder = π × r² × h

Given that the height, h of the cylinder = 9 cm

The radius, r = 5 cm

Volume of the solid cylinder before cutting out the hexagon hole is thus found as follows;

Volume of cylinder = π × 5² × 9 = 706.86 cm³

Volume of hexagon hole = Area of base × height

Where:

Area, A of a regular hexagon of side a =
`(3√(3) )/(2) * a^2`

Therefore, volume of the regular hexagon =
`(3√(3) )/(2) * 2^2 * 9 = 93.53 \ in.^3`

Therefore, the volume of the kaleidoscope (hollow cylinder) = 706.86 - 93.53 = 613.33 in.³.