In a Maths lab there are some cubes and cuboids of the following measurements: i) one cube of side 4 cm ii) one cube of side 6 cm iii) 3 cuboids each of dimensions 4 cm × 4 cm × 6 cm and 3 cuboids each of the dimensions 4 cm × 6 cm × 6 cm A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find the length of side of new cube so formed.

From the given, i) One cube of side = 4 cm We know that volume of a cube = side 3 ∴ Volume = 4 3 = 64 cm 3 ii) One cube of side = 6 cm We know that volume of a cube = side 3 Volume = ( 6 ) 3 = 216 cm 3 iii) 3 cuboids of the size = 4 cm × 4 cm × 6 cm We know that volume of a cuboid= l × b × h Volume of the three cuboids = 4 × 4 × 6 × 3 = 288 cm 3 And 3 cuboid of size 4 cm × 6 cm × 6 cm . Volume of the three cuboids = 4 × 6 × 6 × 3 = 432 cm 3 The total volume of the cubes and cuboids when arranged together = 64 + 216 + 288 + 432 = 1000 cm 3 ∴ The volume of a big single cube = 1000 cm 3 And side = 1000 3 = 10 × 10 × 10 3 = 10 cm Hence, yes it is possible and side = 10 cm .

E M B I B E

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Objective Type Questions>Q 10

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IMPORTANT

Earn 100

The smallest number by which $192$ should be multiplied to make it a perfect cube is

50% studentsanswered this correctly

Important Questions on Cubes and Cube Roots

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ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Objective Type Questions>Q 11

The smallest number by which

686

should be divided to make it a perfect cube is

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IMPORTANT

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Objective Type Questions>Q 12

The volume of a cube is

729 m^{3}

. Length of its side is

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ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Value Based Questions

A school decided to award prizes to their students for three values honesty, punctuality and obedience. If the number of students getting prizes for honesty, punctuality and obedience are in the ratio

1 : 2 : 3

and their product is

162,

find the number of students getting prizes for each value. Which quality you prefer to be rewarded most and why? What values are being promoted?

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IMPORTANT

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Higher Order Thinking Skills (HOTS)>Q 1

Find the volume of a cubical box if the cost of painting of its outer surface is

₹ 1440

at the rate of

₹ 15 per sq . m

.

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IMPORTANT

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Higher Order Thinking Skills (HOTS)>Q 2

In a Maths lab there are some cubes and cuboids of the following measurements:

i) one cube of side $4 cm$

ii) one cube of side $6 cm$

iii) $3$ cuboids each of dimensions $4 cm \times 4 cm \times 6 cm$ and $3$ cuboids each of the dimensions $4 cm \times 6 cm \times 6 cm$

A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find the length of side of new cube so formed.

MEDIUM

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IMPORTANT

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Check Your Progress>Q 1

Show that the number is a perfect cube. Also find the number whose cube is the given number: $74088$

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IMPORTANT

ICSE Understanding Mathematics Class 8>Chapter 4 - Cubes and Cube Roots>Check Your Progress>Q 1

Show that the number is a perfect cube. Also find the number whose cube is the given number: $15625$

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8th ICSE