Volume of Cuboid: Area and Volume of Cuboid and Volume of a Cuboid Prism

Get top class preparation for IAS right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 139K)

A cuboid is a three-dimensional structure having six rectangular faces. These six faces of cuboid exist as a pair of three parallel faces. When the area of the faces of a cuboid is the same, we call this cuboid as a cube. The area of all the faces of a cube is the same as they are all squares.

The capacity of a cuboidal box is basically equal to the volume of cuboid involved.

Volume of Cuboid

Volume of Cuboid

Loading Image

Area and Volume of Cuboid

The total surface area of a cuboid is equal to the sum of the areas of the six rectangular faces whereas the Lateral surface area of a cuboid equal to the sum of the four rectangular faces, in which two rectangular faces of the and bottom faces are excluded. The formula for the total surface area and lateral surface area of a cuboid is given as:

Total Surface Area of a Cuboid square units

Lateral Surface Area of a Cuboid

Now, discuss the volume of a cuboid in detail.

What is the Volume of a Cuboid?

The volume of a three-dimensional shape Cuboid, in general, is equal to the amount of space occupied by the shape cuboid. The term “solid Rectangle” is also known as a cuboid. Because all the faces of a cuboid are rectangular in shape. In rectangular cuboid, all the angles are at right angles and the opposite faces of a cuboid are equal.

The general formula for the calculation of the volume of a cuboid is given below.

The volume of cuboid: The volume of a cuboid is given by the product of its dimensions.

The volume of a cuboid of length ‘l’, breadth ‘b’, height ‘h’ cubic units

Volume of a Cuboid Prism

A cuboid prism or a rectangular prism is the same as the cuboid. It has 6 faces, 8 vertices, and 12 edges. When a cuboid prism or a rectangular prism has a rectangular cross-section. A prism is called right prism when the angle between the base and the sides are at right angles. Also, the top and the bottom surface are in the same shape and size. The volume of the cuboid prims is given as:

Volume of a cuboid prism or rectangular prism, cubic units

Volume of a Cube

Volume of cube: Cuboid in which length of each edge is equal is known as a cube. Thus,

Volume of a cube of side

Problems on Volume of a Cube and Cuboid

Question 1: Calculate the length of the edge of a cube-shaped container of volume

Solution:

  • Here given the cube shaped container which have volume

  • We have formula to find the volume of cube of side

  • Put the value of Cube,

  • We take the cube root of 512.

  • Cuboid in which length of each edge is equal is known as a cube.

  • Hence, the length of cube shaped container is

Question 2: Calculate the amount of air that can be accumulated in a room that has a length of 6 m, breadth of 8 m and a height of 12 m.

  • Amount of air that can be accumulated in a room capacity of the room volume of a cuboid

  • Here given, the value of length, breadth and height is 6 m, 8 m, and 12 m, respectively.

  • And we have the formula of volume of cuboid.

  • Volume of cuboid

  • Put the value of length, breadth, height.

  • Multiplication of 6, 8 and 12.

  • Thus, this room can accommodate the maximum of of air.