Volume of Cuboid Formula

Volume of Cuboid

 

The volume of a solid is the measure of the space occupied by the solid. If it is solid, the space occupied by it is called its volume. If it is hollow, then its interior can be filled by another solid, gas or liquid. In that case, the volume is called the capacity of the object.

The unit of volume (or capacity) is given in cubic units.

 

Let us take 100 cubes of side 1 cm each and arrange them as shown in the following figure.

We observe that the length of the cuboid is 5 cm, the breadth is 5 cm and the height is 4 cm.

So, 5 × 5 × 4 = 100

Volume of 100 cubes of side 1 cm = 100 × (1 × 1 × 1) = 100 cm³

Thus, the volume of the cuboid = 5 × 5 × 4 = 100 cm³

                                                    = (length × breadth × height) cm³

 

Therefore, Volume of a cuboid = l × b × h

 where l is the length, b is the breadth and h is the height of the cuboid.

Volume of Cuboid Formula

Volume of a cuboid = l × b × h

Example 1: Find the volume of a cuboid whose length, breadth and height are 8 cm, 5 cm and 4 cm, respectively.

 

Solution: Here, l = 8 cm, b = 5 cm and h = 4 cm

 Volume of the cuboid = l × b × h = 8 × 5 × 4 = 160 cm³

 

Example 2: If the length, breadth and the volume of a cuboid are 10 cm, 6.5 cm and 520 cm³, respectively, find the height of the cuboid.

Solution: We have, l = 10 cm, b = 6.5 cm and V = 520 cm³

We know that, V = l × b × h

                       520 = 10 × 6.5 × h

                      520 = 65 × h

                          h = 520/65 = 8 cm

Hence, the height of the cuboid is 8 cm.

 

Example 3: The diagonal of a cuboid is 25 cm, breadth is 16 cm and height is 12 cm. Find its length and volume.

 

Solution: Given, diagonal (d) = 25 cm

We know that, d² = l² + b² + h²

(25)² = l² + (16)² + (12)²

l² = (25)² – [(16)² + (12)²] = 625 – 400 = 225

l = 15 cm

Volume of a cuboid = l × b × h = 15 × 16 × 12 cm³ = 2880 cm³

The length of the cuboid is 15 cm and its volume is 2880 cm³.

 

Example 4: The measurement of a brick is 24 cm by 16 cm by 12 cm. Find its volume.

Also, find the number of such bricks that will be required to construct a wall 12 m

high, 4 m wide and 60 cm thick.

 

Solution: Volume of the brick = (24 × 16 × 12) cm³ = 4608 cm³

Volume of the wall = (1200 × 400 × 60) cm³

Number of bricks required = (1200 × 400 × 60)/(24 × 16 × 12) = 6250

Hence, 6250 bricks are required to construct the wall.