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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 15cm by 10cm by 3.5cm. The radius of each of the depressions is 0.5cm and the depth is 1.4cm. Find the volume of wood in the entire stand.

Solution:

Depth (h) of each conical depression = 1.4cm
Radius (r) of each conical depression = 0.5cm
Volume of wood = Volume of cuboid - 4 (Volume of a conical depression)
= l × b × h - 4 × (1/3)πr²h
= 15 × 10 × 3.5 - 4 × (1/3) × (22/7) × (0.5)² × 1.4
= 525 - 1.47
= 523.53 cm³