Ex 12.2, 4
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 (see figure)
Since cones are made inside the cuboid pen stand
Volume of wood in stand = Volume of cuboid Volume of 4 cones
Volume of cuboid
Length = l = 15 cm
Breadth = b = 10 cm
Height = h = 3.5 cm
Volume of cuboid = lbh
= 15 10 3.5 = 525 cm3
Volume of cone
Given radius of each depressions is 0.5 cm and the depth is 1.4 cm
So,
Radius (r) = 0.5 cm
Height (h) = 1.4 cm
Volume of cone = 1/3 2
= 1/3 22/7 0.5 05 1.4
= 1/3 22 0.5 0.5 0.2
= 0.367 cm3
Volume of 4 cones = 4 Volume of 1 cone
= 4 0.367
= 1.47
Now,
Volume of wood in stand = Volume of cuboid Volume of 4 cones
= 525 1.47
= 523.53 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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