Question

Read the following passage and answer the questions given below.

A solid cuboidal toy is made of wood. It has five cone-shaped cavities to hold toy carrots. The dimensions of the toy cuboid are – 10 cm × 10 cm × 8 cm. Each cone carved out – Radius = 2.1 cm and Height = 6 cm

1. Find the volume of wood carved out to make five conical cavities.
2. Find the volume of the wood in the final product.

Answer 1

1. Since,

Volume of cone = `1/3 πr^2h`

Here, r = 2.1 cm and h = 6 cm

∴ Volume of 5 conical cavities = `5 xx 1/3 πr^2h`

= `5 xx 1/3 xx 22/7 xx (2.1)^2 xx 6`

= `(5 xx 22 xx 2.1 xx 2.1 xx 6)/(3 xx 7)` 

= `2910.6/21`

= 138.6 cm³

2. Volume of the wood in the final product = Volume of cuboidal log of wood – Volume of five conical cavities

= (10 × 10 × 8) – 138.6

= 800 – 138.6  ...[∵ Volume of cuboid = l × b × h]

= 661.4 cm³