How many minimum numbers of wooden cuboids of size 2 cm × 3 cm × 4 cm can make a smallest cube? Cutting is allowed. Also find the surface area and volume of cube formed.

To find: Minimum numbers of wooden cuboids of size 2 cm × 3 cm × 4 cm can make a smallest cube. Also find the surface area and volume of cube formed. Now, The least common multiple of 2 , 3 , 4 is 12 Find the dimensions of the cube formed: For the length = 12 ÷ 2 = 6 cm For the height = 12 ÷ 3 = 4 cm For the width = 12 ÷ 4 = 3 cm Hence, the dimensions are 6 cm × 4 cm × 3 cm Volume = length × width × height = 6 × 3 × 4 = 72 cm ³ Surface area = 2 ( length × width ) + 2 ( length × height ) + 2 ( width × height ) = 2 ( 6 × 3 ) + 2 ( 6 × 4 ) + 2 ( 3 × 4 ) = ( 2 × 18 ) + ( 2 × 24 ) + ( 2 × 12 ) = 36 + 48 + 24 = 108 cm ²

A brimful of water cylinder whose radius is 7 cm and height 6 cm . An iron cuboid of size 3 cm × 4 cm × 5 cm is slowly put into it. How much water will drop out? How much water remained in the cylinder?

Given, radius of the cylinder = 7 cm Height of the cylinder = 6 cm Size of the cuboid is 3 cm × 4 cm × 5 cm The amount of the water will drop out = Volume of cuboid 3 cm × 4 cm × 5 cm = 60 cm 3 The amount of water remained in the cylinder = Volume of the cylinder - Volume of the cuboid = πr 2 h - 60 = π 7 2 6 - 60 = 294 π - 60 cm 3

E M B I B E

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 7

EASY

8th Jammu and Kashmir Board

IMPORTANT

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The volume of a cube in ${cm}^{3}$ is equal to curved surface area of a cube in ${cm}^{2}$ , then what is the side of the cube.

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Important Questions on Mensuration

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8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 8

The surface area of a cube is

24 {cm}^{2}

. Two same cubes were joined end to end to form a cuboid. Find the surface area of the cuboid formed.

EASY

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 9

The volume of a cuboid is

27 {cm}^{3}

. Find its surface area.

EASY

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 10

How many minimum numbers of wooden cuboids of size

2 cm \times 3 cm \times 4 cm

can make a smallest cube? Cutting is allowed. Also find the surface area and volume of cube formed.

HARD

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 11

Find the area of trapezium $B O R D$ ; $B O ∥ D R$ in which $B O = 11 cm, B D = 6 cm, D R = 5 cm$ and $R O = 5 cm$ . (correct up to two decimal places)

MEDIUM

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 12

A liquid in a cuboid of size $11 cm \times 9 cm \times 4 cm$ had to be poured into small cylindrical bottles of diameter $4 cm$ and height $3.5 cm$ . How many such bottles are required to empty the cuboid? (Take $π = \frac{22}{7}$ )

HARD

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 13

A brimful of water cylinder whose radius is $7 cm$ and height $6 cm$ . An iron cuboid of size $3 cm \times 4 cm \times 5 cm$ is slowly put into it. How much water will drop out? How much water remained in the cylinder?

MEDIUM

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 10 - Mensuration>Miscellaneous Exercise>Q 14

The radius of a cylinder is doubled and the height is halved. Find the ratio of curved surface areas and volumes of the original cylinder to that of a new cylinder formed?