NCERT Class 5 Maths Chapter 14: How Big How Heavy

Understanding 'How Big' and 'How Heavy'

To understand this chapter, we must first separate the concepts of size (how big) and weight (how heavy).

1. How Big (Volume): This refers to the total 3D space occupied by an object. Even if an object is light, like a big block of sponge, it can have a large volume. We measure volume in cubic units, such as cubic centimetres ($cm^3$ or cu cm).
2. How Heavy (Weight): This represents the mass of an object, or how strongly gravity pulls it down. A small lead ball has a small volume but can be very heavy. We measure weight in grams ($g$) and kilograms ($kg$).

In this chapter, we often compare volumes by seeing how many standard objects (like $1\text{ cm}$ cubes, marbles, or matchboxes) can fit inside a larger container.

How to Measure the Volume of a Cuboid Box

1. Identify the Dimensions — Find the length ($l$), width ($b$), and height ($h$) of the rectangular box or cuboid. Make sure all measurements are in the same unit, like centimetres (cm).
2. Use the Cuboid Volume Formula — The formula to find the volume is: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$.
3. Calculate and Write the Unit — Multiply the three numbers together. Always write the final answer in cubic units, such as cubic cm ($cm^3$).

Key Formulas and Measurement Units

• Volume of a Cube = $\text{Side} \times \text{Side} \times \text{Side}$
• Volume of a Cuboid = $\text{Length} \times \text{Breadth} \times \text{Height}$
• Unit Conversion for Weight: $1\text{ kg} = 1000\text{ grams (g)}$
• To convert kilograms to grams, multiply by 1000. To convert grams to kilograms, divide by 1000.

Common Mistakes to Avoid in Exams

• Confusing Area and Volume: Remember that Area is 2-dimensional (flat space, measured in $cm^2$), whereas Volume is 3-dimensional (solid space, measured in $cm^3$). Do not write $cm^2$ for volume answers!
• Ignoring Unit Alignment: Always check if all sides are in the same units (either all cm or all m) before multiplying. If they are different, convert them first.

Practice Questions with Solutions

• Q: A matchbox measures $5\text{ cm}$ in length, $3\text{ cm}$ in width, and $1\text{ cm}$ in height. What is its volume?
  A: Step 1: Write down the given dimensions:
  Length ($l$) = $5\text{ cm}$
  Width ($b$) = $3\text{ cm}$
  Height ($h$) = $1\text{ cm}$

  Step 2: Use the formula for the volume of a cuboid:
  $\text{Volume} = l \times b \times h$

  Step 3: Calculate the product:
  $\text{Volume} = 5 \times 3 \times 1 = 15$

  Final answer: The volume of the matchbox is $15\text{ cubic cm}$ (or $15\text{ cm}^3$).

• Q: A large box has a volume of $240\text{ cubic cm}$. If the volume of one soap cake is $30\text{ cubic cm}$, how many soap cakes can fit inside the large box?
  A: Step 1: Identify total volume and unit volume:
  Total volume of box = $240\text{ cm}^3$
  Volume of one soap cake = $30\text{ cm}^3$

  Step 2: Set up the division to find the total number of soap cakes:
  $\text{Number of soap cakes} = \frac{\text{Total Volume}}{\text{Volume of one soap cake}}$

  Step 3: Calculate:
  $\text{Number} = \frac{240}{30} = 8$

  Final answer: $8$ soap cakes can fit inside the box.

• Q: Raman has a bag of flour weighing $4.5\text{ kg}$. What is the weight of the flour in grams?
  A: Step 1: Use the relation between kilograms and grams:
  $1\text{ kg} = 1000\text{ g}$

  Step 2: Multiply the weight in kg by 1000 to convert to grams:
  $\text{Weight in grams} = 4.5 \times 1000$

  Step 3: Calculate the value:
  $4.5 \times 1000 = 4500$

  Final answer: The weight of the flour is $4500\text{ grams}$.

• Q: A cubical water tank has each side measuring $2\text{ metres}$. Find the volume of the tank in cubic metres.
  A: Step 1: Note the side of the cube:
  $\text{Side} = 2\text{ m}$

  Step 2: Apply the volume formula for a cube:
  $\text{Volume} = \text{Side} \times \text{Side} \times \text{Side}$

  Step 3: Calculate:
  $\text{Volume} = 2 \times 2 \times 2 = 8$

  Final answer: The volume of the tank is $8\text{ cubic metres}$ (or $8\text{ m}^3$).

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