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Volume of Cubes and Rectangular Prisms

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How do you write the volume of a cuboid or rectangular prism?

Cuboids are rectangular boxes with different length sides. It has six faces and all angles form right angles.

And all of its faces are rectangles.

It is also called a prism as it has the same cross-section throughout the length. It can be also termed as a rectangular prism.

Example: Calculate the volume of cuboid of length 22 cm, height 10 cm and width 8 cm.

Volume = L × H × W

Volume of cuboid = 22 × 10 × 8 = 1760 cm3

How do you write the volume of a cube?

A cube is a box with 6 faces which has equal side lengths all over. Each face of the cube is a square. So, the length, width and height of a cube are all same.

Example: Jill is packing a carton box with confetti’s. She wants to know the volume of the cubical box to fill it up. She knows that the side of box measures 4 cm.

Volume of cube is denoted by a³ which means side × side × side where side = a.

So, volume of the carton box = a³ = 4³ = 4 × 4 × 4 = 64 cm³

Square Prism

When any two sides of a cuboid are same, it can also be called as a square prism

 

  1. Find the volume of a cube of side 3 cm.
  2. What is the volume of a swimming pool if length is 40 m, width is 56 m, and depth is 22 m?

  1. Jerald wants to find out the volume of a metallic tool box which has a width of 11 cm, depth of 8 cm and length of 9 cm.

  1. What is the volume of a wooden dice of side of length 5 mm?

  1. A cube has a volume of 81 cm3. What is the length of each side of the cube?
Answer key
  1. 27 cm3
  2. 49280 m3
  3. 792 cm3
  4. 125 mm3
  5. 9 cm

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