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How Big How Heavy - Volume of Cubes and Cuboids

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Volume is the measure of the total space occupied by a three-dimensional object. Imagine filling a hollow container with water or sand; the amount of substance it holds represents its volume.

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A cuboid is a solid shape with six rectangular faces, similar to a brick or a matchbox. It is defined by three distinct dimensions: Length (LL), Breadth or Width (BB), and Height (HH).

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A cube is a special type of cuboid where all sides (edges) are equal in length. You can visualize this as a standard playing die or a Rubik's cube where the length, breadth, and height are identical.

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The standard unit of volume is the cubic unit. A small 'unit cube' measuring 1 cm1\text{ cm} on all sides has a volume of 1 cubic centimeter1\text{ cubic centimeter} (1 cm31\text{ cm}^3).

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To find the volume of a larger cuboid visually, imagine it as a building made of smaller unit cubes. If the floor (base) has 44 rows of 55 cubes each, and the building is 33 floors (layers) high, the volume is the total number of cubes used.

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There is a direct relationship between volume and capacity. For example, a container with a volume of 1000 cm31000\text{ cm}^3 can hold exactly 1 litre1\text{ litre} of liquid, and 1 cm31\text{ cm}^3 is equivalent to 1 ml1\text{ ml}.

📐Formulae

Volume of a Cuboid=Length×Breadth×Height\text{Volume of a Cuboid} = \text{Length} \times \text{Breadth} \times \text{Height}

Volume of a Cube=Side×Side×Side=(Side)3\text{Volume of a Cube} = \text{Side} \times \text{Side} \times \text{Side} = (\text{Side})^3

1 litre=1000 ml1\text{ litre} = 1000\text{ ml}

1 cm3=1 ml1\text{ cm}^3 = 1\text{ ml}

1000 cm3=1 litre1000\text{ cm}^3 = 1\text{ litre}

💡Examples

Problem 1:

A rectangular fish tank has a length of 40 cm40\text{ cm}, a breadth of 20 cm20\text{ cm}, and a height of 25 cm25\text{ cm}. Calculate the volume of water the tank can hold in cubic centimeters.

Solution:

Given dimensions: Length (LL) = 40 cm40\text{ cm} Breadth (BB) = 20 cm20\text{ cm} Height (HH) = 25 cm25\text{ cm}

Using the formula: Volume=L×B×H\text{Volume} = L \times B \times H Volume=40 cm×20 cm×25 cm\text{Volume} = 40\text{ cm} \times 20\text{ cm} \times 25\text{ cm} Volume=800×25\text{Volume} = 800 \times 25 Volume=20,000 cm3\text{Volume} = 20,000\text{ cm}^3

Explanation:

To find the volume of the cuboid-shaped tank, we multiply the three dimensions (length, breadth, and height) together. The resulting value represents the total space inside the tank.

Problem 2:

Find the volume of a wooden cube if the length of one of its edges is 6 cm6\text{ cm}.

Solution:

Given: Side (ss) = 6 cm6\text{ cm}

Using the formula for the volume of a cube: Volume=s×s×s\text{Volume} = s \times s \times s Volume=6 cm×6 cm×6 cm\text{Volume} = 6\text{ cm} \times 6\text{ cm} \times 6\text{ cm} Volume=36×6\text{Volume} = 36 \times 6 Volume=216 cm3\text{Volume} = 216\text{ cm}^3

Explanation:

Since all sides of a cube are equal, we multiply the side length by itself three times to find the total space it occupies.