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Materials Around Us - Space and Volume

Grade 6CBSE

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

🔑Concepts

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Matter is defined as anything that has mass and occupies space. The space occupied by an object is called its volume.

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The SI unit of volume is the cubic metre (m3m^3), but for smaller objects, we often use cubic centimetres (cm3cm^3).

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Liquids are measured in Litres (LL) and Millilitres (mLmL). The relationship between these units is 1L=1000mL1 L = 1000 mL.

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There is a direct relationship between liquid capacity and solid volume: 1mL=1cm31 mL = 1 cm^3.

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The volume of regular solid objects, like a rectangular box (cuboid), is calculated by multiplying its length (ll), breadth (bb), and height (hh).

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The volume of irregular solids (like a stone) is measured using the water displacement method. When an object is submerged in water, it displaces a volume of water equal to its own volume.

📐Formulae

Volume of a Cuboid=l×b×h\text{Volume of a Cuboid} = l \times b \times h

1 Litre=1000 mL1 \text{ Litre} = 1000 \text{ mL}

1 mL=1 cm31 \text{ mL} = 1 \text{ cm}^3

Volume of irregular object=V2−V1\text{Volume of irregular object} = V_2 - V_1

💡Examples

Problem 1:

Calculate the volume of a brick that has a length of 10 cm10 \text{ cm}, a breadth of 5 cm5 \text{ cm}, and a height of 3 cm3 \text{ cm}.

Solution:

V=10 cm×5 cm×3 cm=150 cm3V = 10 \text{ cm} \times 5 \text{ cm} \times 3 \text{ cm} = 150 \text{ cm}^3

Explanation:

To find the volume of a regular rectangular object, we multiply the three dimensions: length, breadth, and height.

Problem 2:

A measuring cylinder is filled with water to the 60 mL60 \text{ mL} mark. After a small stone is lowered into the water, the level rises to 85 mL85 \text{ mL}. What is the volume of the stone?

Solution:

85 mL−60 mL25 mL\begin{array}{r} 85 \text{ mL} \\ - 60 \text{ mL} \\ \hline 25 \text{ mL} \end{array} Therefore, Volume of stone = 25 cm325 \text{ cm}^3.

Explanation:

Using the water displacement method, the volume of the stone is the difference between the final volume (V2V_2) and the initial volume (V1V_1). Since 1 mL=1 cm31 \text{ mL} = 1 \text{ cm}^3, the volume is 25 cm325 \text{ cm}^3.

Problem 3:

Convert 4.5 Litres4.5 \text{ Litres} into millilitres.

Solution:

4.5×1000=4500 mL4.5 \times 1000 = 4500 \text{ mL}

Explanation:

Since 1 L=1000 mL1 \text{ L} = 1000 \text{ mL}, we multiply the value in Litres by 10001000 to get the value in millilitres.