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Cubes and Cuboids Questions and Answers

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Bancroft’s School - Sample 11+ Maths Paper 2020 Question 24, Geometry, Cubes and Cuboids, Logical Problems

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Forest School - 11 Plus Maths Sample Paper 1 - 2020 Question 36, Geometry, Cubes and Cuboids, Logical Problems

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Streatham and Clapham High School - 11+ Maths Entrance Exam Section A and B 2019 Question 35, Numbers, Word Problems, Logical Problems, Geometry, Cubes and Cuboids

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Aldenham School - 11+ Maths Sample Paper 2019 Question 20, Geometry, 3D Shapes, Volume, Cubes and Cuboids, Logical Problems

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St Albans School - 11 Plus Maths Entrance Exam Paper 2019 Question 16, Geometry, Volume, Area & Perimeter, Cubes and Cuboids

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St Albans School - 11 Plus Maths Entrance Exam Paper 2019 Question 15, Geometry, Volume, Area & Perimeter, Cubes and Cuboids

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The Manchester Grammar School 11 Plus Papers Arithmetic A - 2019 Question 17, Numbers, Word Problems, Geometry, Cubes and Cuboids, 3D Shapes, Volume

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The Manchester Grammar School 11 Plus Papers Arithmetic A - 2019 Question 15, Geometry, Nets of Solids, Area & Perimeter, Cubes and Cuboids, 3D Shapes

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Geometry, Cubes and Cuboids, Volume, Logical problems

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Cubes and Cuboids and Volume

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Ratio & Proportion, Cubes and Cuboids, Volume and Cube numbers

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Factors, Cubes and Cuboids and Logical Problems

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Volume, Cubes and Cuboids and Word Problems

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Cubes and Cuboids and Nets of solids

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3D shapes and Cubes and Cuboids

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Cubes and Cuboids and Volume

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Cubes and Cuboids and Logical Problems

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Area and Perimeter, Rectangle, Cubes and Cuboids, Volume and Word Problems

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Addition, Subtraction, Cubes and Cuboids and Logical Problems

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Properties of Cubes and Cuboids for 11 plus Exam

1. Properties of Cube

Cube: The cube is one of the simplest three-dimensional shapes with the dimensions length, width, and height all of the same size. It has six-square faces, eight vertices, and twelve edges. 

Some real-life examples of cubes are Rubik’s cube, 6-sided dice, etc.

11+ Topicwise Cubes and Cuboids Article image 1

2. Properties of Cuboid

Cuboids: A cuboid is a three-dimensional shape with the dimensions as length, width and height. It has six rectangular faces, eight vertices and twelve edges.

Some simple real-life examples of cuboids are bricks, lunch box, etc.

11+ Topicwise Cubes and Cuboids Article image 2

3. Area and Volume formulas of Cube and Cuboid

Cube 

11+ Topicwise Cubes and Cuboids Article image 3

Side of the cube is a.

Surface area of the cube = 6a²

Volume of the cube = a³

Cuboid 

11+ Topicwise Cubes and Cuboids Article image 4

l, w and h are the dimensions of cuboid

Surface area of cuboid = 2(lw+wh+lh)

Volume of cuboid = l × h

3.1 Example Question on Area and Volume of Cube

Surface area of a cube is 96 cm². Work out the edge and volume of this cube.

Solution :

Surface area of a cube = 6a²

                               96 = 6a²   

                               a² = 96 ÷ 6

                               a² = 16

                          a × a = 4 × 4

                                a = 4 cm

Side of the cube is 4 cm

Volume of a cube = a³

                             = (4)³

                             = 4 × 4 × 4

                             = 64 cm³

3.2 Example Question on Area and Volume of Cuboid

Calculate the volume and surface area of the cuboid shown below.

11+ Topicwise Cubes and Cuboids Article image 5

Solution:

Length of Cuboid (l) =  20 mm

Width of Cuboid  (w) =  4 mm

Height of Cuboid (h) =  12 mm

Volume of Cuboid = l ×w × h

                             = 20 × 4 × 12

                             = 960 mm³

Surface area of cuboid =  2(lw + wh + lh)

                                     = 2 (20 × 4 + 4 × 12 + 12 × 20)

                                     = 2(80 + 48 + 240)

                                     = 368 mm²

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