Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer 1

Volume of one conical depression = 1/3 x πr² h

= 1/3 x 22/7 x 0.5² x 1.4 cm³ = 0.366 cm³

Volume of 4 conical depression = 4 x 0.366 cm³

= 1.464 cm³

Volume of cuboidal box = L x B x H

= 15 x 10 x 3.5 cm³ = 525 cm³

Remaining volume of box = Volume of cuboidal box – Volume of 4 conical depressions

= 525 cm³ − 1.464 cm³ = 523.5 cm³