Volume of Cubes and Cuboids | Formulas, Questions on Volume of Cube, Cuboid

Cube and Cuboids are three-dimensional shapes that have six faces, eight vertices, and twelve edges. The volume of a three-dimensional figure is the number of cubes required to fill the object. It is defined as the side times side. Get the definition, formulas, standard units, and example problems in the following sections.

What is Meant by Volume?

The volume of any three-dimensional solid shape is the measurement of the space occupied by the object. For a hollow 3-dimensional figure, the volume of the object is the difference in space occupied by the body and the amount of space inside a body. The interior capacity of a solid is also called the volume of a substance.

The measuring units of volume are cubic units. Those can be cm³, m³. The volume can also be measured in liters, milliliters, millimeters.

Standard Units of Volume

The volume is always measured in cubic units. The standard unit is cm³, m³, mm³, but various other units of length measurement are m, dm, dam, etc.

Cuboid

The cuboid is a polyhedron made up of six rectangular faces, eight vertices, and twelve edges. The faces of the cuboid are parallel. But all the faces are not equal in dimensions.

The properties of a cuboid are

  • Every cuboid has six rectangles, each rectangle is called the face.
  • It has top faces, bottom faces. Other than the top, bottom faces are called the adjacent faces.
  • It has 12 edges and opposite sides of the rectangle are equal.
  • The point of intersection of 3 edges of a cuboid is called the vertex.
  • And it has 8 vertices.

Volume of Cuboid

The volume of the cuboid is the product of the area of one surface and height. Let us take l, b, h as the length, breadth, and height of the cuboid.

Area of the rectangular base = (l x b)

The volume of the cuboid = (Area of the base) x height

= (l x b) x h

Volume = lbh

Then,

Length of the Cuboid = (volume) / (breadth x height)

Breadth of the Cuboid = (Volume) / (length x height)

Height of the cuboid = (Volume) / (length x breadth)

Cube

Cube is a special type of cuboid where length, breadth and height are equal.

The properties of Cube are as follows:

  • It has six faces and twelve edges of equal length.
  • The shape of all faces of the cube is in square shape.
  • The angles of the cube in the plane are at a right angle.
  • Each face of the cube meets four other faces.
  • Opposite edges are parallel to each other.
  • The vertex of the cube meets three faces and edges.

Volume of Cube

The volume of a cube is nothing but the number of cubic units occupied by the cube completely.

Volume of cube = a x a x a = a³

Example Questions on Volume of Cubes and Cuboids

Example 1.

If the length, breadth, and height of the cuboid are 10 cm, 14 cm, 9 cm, then find its volume?

Solution:

Given that,

Length of the cuboid l = 10 cm

Breadth of the cuboid b = 14 cm

Height of the cuboid h = 9 cm

The volume of cuboid = lbh

Volume = 10 x 14 x 9 = 1260 cm³.

Example 2.

Find the volume of the cube, having a side length of 6 cm?

Solution:

Given that,

Side length of cube a = 6 cm

The volume of cube = a³

Volume = 6³ = 6 x 6 x 6 = 216 cm³.

Example 3.

Calculate volume, the perimeter of the cube whose side length is 14 cm?

Solution:

Given that,

Side length of cube a = 14 cm

The volume of the cube formula is

Volume = a³

Volume V = 14³

= 14 x 14 x 14 = 2744 cm³

The perimeter of the cube formula is

Perimeter = 12a

= 12 x 14 = 168 cm

Therefore, the perimeter and volume of the cube is 168 cm, 2744 cm³

FAQS on Volume of Cubes and Cuboids

1. What are the formulas of cube and cuboid volume?

The volume of the cuboid is defined as the product of length, height, and breath.

Cuboid volume V = length x breadth x height.

Cube volume = side³

2. What is the difference between cuboid and cube?

The sides of the cube are in equal length but the cuboid sides are different. The faces of the cube are in a square shape, the faces of the cuboid are in a rectangle shape. All diagonals of the cube are equal but the cuboid has equal diagonals for parallel sides.

3. What is the perimeter of the cube and cuboid?

Perimeter of cuboid = 4(length + breadth + height)

Perimeter of cube = 12 x length.

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