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

Answer:

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

Step-by-step 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 = $\frac{3\sqrt{3} }{2} \times a^2$

Therefore, volume of the regular hexagon = $\frac{3\sqrt{3} }{2} \times 2^2 \times 9 = 93.53 \ in.^3$

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