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How Big How Heavy - Measuring Weight and Capacity

Grade 5CBSE

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

🔑Concepts

Volume is the total amount of space occupied by a three-dimensional object. Imagine a hollow box; the amount of space inside it that can be filled with air or water is its volume.

The basic unit of volume is the cubic centimeter, written as 1cm31 cm^3. Visually, this is a tiny cube where the length, width, and height are all exactly 1cm1 cm. For larger objects, we use cubic meters (m3m^3).

A cuboid is a 3D shape like a shoebox or a brick. To find its volume, you must consider three dimensions: Length (how long it is), Breadth (how wide it is), and Height (how tall it is).

A cube is a special cuboid where all sides are equal, like a playing die. Since the length, breadth, and height are the same, we simply multiply the side by itself three times.

Capacity is a term used for the volume of liquids a container can hold. While solid volume is measured in cm3cm^3, liquid capacity is measured in Liters (LL) and Milliliters (mLmL). Think of a large milk packet as 1L1 L and a small medicine dropper as holding 1mL1 mL.

The displacement method is used to measure the volume of irregular objects like stones. When you drop a stone into a measuring jar filled with water, the water level rises. The volume of the displaced (risen) water is exactly equal to the volume of the stone.

Weight measures how heavy an object is using units like grams (gg) and kilograms (kgkg). In many contexts, 1mL1 mL of water has a mass of approximately 1g1 g, and 1000mL1000 mL (or 1L1 L) of water weighs approximately 1kg1 kg.

📐Formulae

Volume of a Cuboid=Length×Breadth×HeightVolume\ of\ a\ Cuboid = Length \times Breadth \times Height

Volume of a Cube=Side×Side×Side=s3Volume\ of\ a\ Cube = Side \times Side \times Side = s^3

1 Kilogram (kg)=1000 Grams (g)1\ Kilogram\ (kg) = 1000\ Grams\ (g)

1 Liter (L)=1000 Milliliters (mL)1\ Liter\ (L) = 1000\ Milliliters\ (mL)

1 cubic centimeter (cm3)=1 Milliliter (mL)1\ cubic\ centimeter\ (cm^3) = 1\ Milliliter\ (mL)

💡Examples

Problem 1:

A water tank is in the shape of a cuboid. Its length is 10cm10 cm, breadth is 8cm8 cm, and height is 5cm5 cm. Calculate the volume of water it can hold in cm3cm^3 and mLmL.

Solution:

  1. Identify the dimensions: Length=10cmLength = 10 cm, Breadth=8cmBreadth = 8 cm, Height=5cmHeight = 5 cm. \ 2. Use the formula for the volume of a cuboid: Volume=L×B×HVolume = L \times B \times H. \ 3. Substitute the values: Volume=10×8×5=400cm3Volume = 10 \times 8 \times 5 = 400 cm^3. \ 4. Since 1cm3=1mL1 cm^3 = 1 mL, the capacity in mLmL is 400mL400 mL.

Explanation:

We calculate the total space inside the tank by multiplying its three dimensions and then use the direct conversion between cubic centimeters and milliliters.

Problem 2:

A sack of rice weighs 5kg5 kg and 250g250 g. If a shopkeeper sells 2kg2 kg and 750g750 g from it, how much rice is left in the sack?

Solution:

  1. Convert the total weight to grams: 5kg 250g=(5×1000)+250=5250g5 kg\ 250 g = (5 \times 1000) + 250 = 5250 g. \ 2. Convert the sold weight to grams: 2kg 750g=(2×1000)+750=2750g2 kg\ 750 g = (2 \times 1000) + 750 = 2750 g. \ 3. Subtract the sold amount from the total: 5250g2750g=2500g5250 g - 2750 g = 2500 g. \ 4. Convert back to kgkg: 2500g=2kg 500g2500 g = 2 kg\ 500 g.

Explanation:

To solve weight subtraction problems easily, it is best to convert everything into the smaller unit (grams) first, perform the subtraction, and then convert back to kilograms and grams.