CBSE Class 5 Mathematics NCERT Solutions: How Big How Heavy

To answer this question, we need to compare the volume of 10 five-rupee coins with the volume of 10 marbles. Generally, coins are denser and have a different shape than marbles. Without specific measurements or a direct comparison tool, it's a guess. However, based on typical sizes and shapes, it is likely that 10 five-rupee coins might occupy a similar or slightly less volume than 10 marbles, depending on how they are packed. The provided examples give us a sense of relative volumes for other items compared to marbles.

Guess: The volume of 10 five-rupee coins will likely be less than or about the same as the volume of 10 marbles.

This question involves a practical activity. Students are asked to create their own measuring glass using marbles. Here's how to perform the activity and what the table represents:

1. Create the Measuring Glass: Take a glass and fill it with water up to a certain level. Mark this level as 'O'. Carefully add 5 marbles and mark the new water level as '5 M'. Continue adding marbles in batches of 5 and marking the water level (10 M, 15 M, 20 M, 25 M, 30 M, 35 M). This creates a scale where each mark represents the volume of a certain number of marbles.
2. Measure Other Objects: Now, take different objects (like a matchbox filled with sand, a stone, an orange, an apple) and place them one by one into the measuring glass. Observe how much the water level rises. Estimate how many marbles correspond to this rise in water level.
3. Fill the Table: Record the name of the object and its estimated volume in marbles. The table provided shows example measurements:
   • Matchbox with sand: Approximately 7 marbles
   • A stone: Approximately 4 marbles
   • An orange: Approximately 15 marbles
   • An apple: Approximately 16 marbles

This activity helps in understanding that different objects have different volumes and allows for estimation using a non-standard unit (marbles).

This section uses a measuring bottle (or glass) to determine the volume of objects in milliliters (mL). Here are the solutions to each part:

1. The volume of 6 marbles is given as 7 mL.
2. The volume of 16 one-rupee coins is given as 18 mL.
3. The volume of 24 marbles is given as 28 mL.
4. The volume of 32 one-rupee coins is given as 36 mL.
5. Mollie puts five-rupee coins into the measuring bottle:
   • If 30 mL of water is pushed up, she has put in 27 coins. This implies that each five-rupee coin displaces approximately $30\; \backslash text\{\; mL\}\; /\; 27\; \backslash approx\; 1.11\; \backslash text\{\; mL\}$ of water.
   • If 60 mL of water is pushed up, she has put in 54 coins. This is consistent with the previous calculation, as $54\; \backslash text\{\; coins\}\; \backslash times\; 1.11\; \backslash text\{\; mL/coin\}\; \backslash approx\; 60\; \backslash text\{\; mL\}$.
6. Here are the volumes in mL for some other things, measured using the bottle:
   • A scale: 6 mL
   • A tumbler: 22 mL
   • A pair of scissors: 8 mL
   • A pen: 6 mL
7. Guess how many litres of water your body will push up? The answer is estimated to be about 30 L. This is a very rough estimate of human body volume.

This part introduces the concept of volume using cubic centimeters (cm cubes) and relates it to the dimensions of a book.

• Length: The book is 26 cm long, so 26 cubes of 1 cm side length (1 cm cubes) can fit along its length.
• Width: The book is 26 cm wide, so 26 cubes of 1 cm side length can fit along its width.
• Total Cubes on the Book: The problem states that 520 cm cubes fit on the book. This implies the book's surface area is covered by these cubes. The calculation shown is (26 x 20 = 520 cubes). This suggests the book might be 26 cm long, 20 cm wide, and 1 cm thick, or it refers to the number of cubes that can be placed on its surface if arranged in layers. Assuming it refers to the surface coverage, the calculation implies a width of 20 cm if the length is 26 cm, or vice versa, to get 520 cubes on the surface. However, the text also says it's 26 cm wide, which seems contradictory unless the 20 is a typo and it should be 26x26 for surface coverage, or the 520 refers to cubes filling a certain volume. Let's follow the given calculation: 26 cm length x 20 cm width = 520 cm cubes on the surface.
• Arrangement in a Line: If all 520 cm cubes are arranged in one single line, end-to-end, the total length of that line would be 520 cm. This is because each cube is 1 cm long, so 520 cubes placed side-by-side would form a line 520 cm long.

This question builds upon the previous one, using the volume of a Math-Magic book to calculate the volume of a stage made of multiple books and then asking for estimations of other objects in cm cubes.

• Volume of the Stage: The stage is made of 5 Math-Magic books. Since each book has a volume equivalent to 520 cm cubes (as calculated in the previous question, assuming this refers to the volume of one book), the total volume of the stage is calculated as: $520\; \backslash text\{\; cm\; cubes/book\}\; \backslash times\; 5\; \backslash text\{\; books\}\; =\; 2600\; \backslash text\{\; cm\; cubes\}$.
• Volume of a Matchbox: The question asks to guess the volume of a matchbox in cm cubes. The provided answer is that a matchbox is about 24 cm cubes. This is an estimation, as the actual volume would depend on the specific dimensions of the matchbox.

This section emphasizes estimation and the use of a standard unit (cm cubes) for measuring volume.