**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 cm^{3}

Thus, the volume of the cuboid = 5 × 5
× 4 = 100 cm^{3}

= (length × breadth × height) cm^{3}

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

**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

* *= 8 × 5 ×
4 = 160 cm^{3}

**Example 2:** If the length,
breadth and the volume of a cuboid are 10 cm, 6.5 cm and 520 cm^{3},
respectively, find the height of the cuboid.

**Solution:** We have, l = 10
cm, b = 6.5 cm and V = 520 cm^{3}

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, *d*^{2} = *l*^{2}
+ *b*^{2} + *h*^{2}

(25)^{2} = *l*^{2}
+ (16)^{2} + (12)^{2}

*l*^{2}
= (25)^{2} – [(16)^{2} + (12)^{2}] = 625 – 400 = 225

*l *= 15 cm

Volume of a cuboid = *l × b × h = *15
× 16 × 12 cm^{3} = 2880 cm^{3}

The length of the cuboid is 15 cm and its volume
is 2880 cm^{3}.

**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) cm^{3} = 4608 cm^{3}

Volume of the wall = (1200 × 400 × 60) cm^{3 }

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

Hence, 6250 bricks are required to construct the
wall.