CLASS-6
VOLUME OF CUBOID

Start with bottom, which is a rectangle of size 5 cm by 3 cm, so the area of the base 15 cm² and so it is possible to cover it with 15 cubes, each with side 1 cm.

This forms the bottom layer of the solid and it has a height of 1 cm.

Now, on top of each unit cube in the bottom layer, place another unit cube to form a second layer. The solid thus formed has a height of 2 cm and it contains 15 X 2 units = 30 units cube.

Hence, a cuboid with dimensions 5 cm by 3 cm by 2 cm has a volume of 30 cm³. It follows that,  if a cuboid has length l units, breadth b units, and height h units, then the volume of the cuboid is = l units X b units X h units = (l X b X h) units³

So, volume of the cuboid (V) = (l X b X h) units³

The volume of a cuboid (rectangular prism) can be calculated using the following formula:

Volume = length (l) × width (w) × height (h)

Where:

• l represents the length of the cuboid.
• w represents the width of the cuboid.
• h represents the height of the cuboid.

To find the volume of a cuboid, simply multiply these three dimensions together.

Here are a couple of examples to illustrate how to calculate the volume of a cuboid:

Example.1) Let's say you have a rectangular box (cuboid) with the following dimensions:

• Length (l) = 6 meters
• Width (w) = 4 meters
• Height (h) = 3 meters

Ans.)

To find the volume of this cuboid, you would use the formula:

Volume = l × w × h

Volume = 6 meters × 4 meters × 3 meters

Volume = 72 cubic meters

So, the volume of this cuboid is 72 cubic meters.    (Ans.)

Example.2) Suppose you have a rectangular storage container with these measurements:

• Length (l) = 10 feet
• Width (w) = 8 feet
• Height (h) = 2 feet

Ans.)

To calculate the volume, apply the formula:

Volume = l × w × h

Volume = 10 feet × 8 feet × 2 feet

Volume = 160 cubic feet

The volume of this rectangular storage container is 160 cubic feet. (Ans.)