Ex 11.4, 4 A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Given,
Length of cuboid = l = 60 cm
Breadth = b = 54 cm
& Height = h = 30 cm
Also, Side of cube = 6 cm
Now,
Cube is placed in the cuboid
So,
Volume of cuboid = Number of cubes × Volume of 1 cube
Number of cubes = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑐𝑢𝑏𝑒)
Volume of cuboid
Volume = 𝑙×𝑏×ℎ
= 60×54×30
= 6×54×3×100
= 18×54×100
= 972×100
= 97200 cm3
Volume of cube
Volume = (Side)3
= 6×6×6
= 216 cm3
Now,
Number of cubes = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑐𝑢𝑏𝑒)
= 97200/216
= 16200/36 = 2700/6
= 450
∴ 450 small cubes can be placed in cuboid.

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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