Question

A wooden box is in the shape of a cuboid with three conical depressions. 7 cm × 3 cm × 4 cm are the dimensions of the cuboid and the radius and depth of the conical depressions are 0.5 cm and 1.2 cm. Find the volume of the entire wooden box?

(a) 109.4 cm^3

(b) 80.05 cm^3

(c) 150 cm^3

(d) 89.4 cm^3

I got this question by my college professor while I was bunking the class.

My question comes from Surface Area and Volume of Combination of Solids topic in chapter Surface Area and Volumes of Mathematics – Class 10

Answer 1

Correct choice is (b) 80.05 cm^3

Explanation: Volume of the wooden box = volume of the cuboid – the volume of 3 conical depressions

= lbh – 3(\(\frac {1}{3}\)πr^2h)

= (7 × 3 × 4) – 3(\(\frac {1}{3}\) × 3.14 × 0.5^2 × 1.2)

= 80.05 cm^3