Question

A pen stand made of wood is in the shape of a cuboid with 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.

(a) 532.54 cm³ 

(b) 523.54 cm³ 

(c) 534.54 cm³ 

(d) 543.54 cm³

Answer 1

Answer: (b) = 523.54 cm³  

Volume of wood in the entire stand = Volume of cuboidal stand – Volume of 4 conical depressions

= l × b × h – 4 × \(\frac{1}{3}\) πr²h 

= 15 × 10 × 3.5 - 4 × \(\frac{1}{3}\) × \(\frac{22}{7}\) × (0.5)² × 1.4 

= 525 - 1.46 cm³

= 523.54 cm³