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Q1. Find the volume of a cuboid of length 4 cm, breadth 2 cm and height 3 cm?
Ans: The volume of a cuboid can be calculated using the formula:
- Volume = length (l) × breadth (b) × height (h)
Given the dimensions:
- Length = 4 cm
- Breadth = 2 cm
- Height = 3 cm
Substituting the values into the formula:
- Volume = 4 cm × 2 cm × 3 cm = 24 cubic centimetres (cu cm)
Thus, the volume of the cuboid is 24 cu cm.
Q2. A water tank has length 9 cm, breadth 7 cm and height 5 cm. How many cubic metre of water can it hold?
Ans: Given the dimensions of the water tank:
- Length (l) = 9 cm
- Breadth (b) = 7 cm
- Height (h) = 5 cm
The volume of the tank can be calculated using the formula: Volume = l × b × h = 9 cm × 7 cm × 5 cm = 315 cubic centimetres (cu cm).
To convert this volume into cubic metres, we use the conversion factor where 1 cubic metre equals 1,000,000 cubic centimetres: Therefore, the volume in cubic metres is: Volume in cubic metres = 315 cu cm / 1,000,000 = 0.000315 cubic metres.
Q3. Find the volume of a cuboid of side 8cm x 6 cm x 5 cm and a cube of side 9 cm.
Ans: The volume of a cuboid can be calculated using the formula: Volume of a cuboid = length (l) × breadth (b) × height (h) For the given cuboid:
- l = 8 cm
- b = 6 cm
- h = 5 cm
Thus, the volume is: Volume of a cuboid = 8 cm × 6 cm × 5 cm = 240 cm³
For the cube, the volume can be calculated using the formula: Volume of a cube = side × side × side For the cube:
- side = 9 cm
Therefore, the volume is: Volume of a cube = 9 cm × 9 cm × 9 cm = 729 cm³ In conclusion, the cuboid has a volume of 240 cm³, while the cube has a greater volume of 729 cm³.
Q4. A 2 rupee coin weighs 6g. What is the weight of a sack with:
(a) 1500 coins?
(b) 3000 coins?
Ans: Weight of a two-rupee coin = 6 g
- (a) Weight of a sack with 1500 coins = 1500 x 6 = 9000 g = 9 kg
- (b) Weight of a sack with 3000 coins = 3000 x 6 = 18000 g = 18 kg
Q5. The length, breadth and height of the inside of a rectangular box are 100 cm, 80 cm and 60 cm. How many centimeter cubes can be fitted in that box?
Ans: Given the dimensions of the rectangular box:
- Length (l) = 100 cm
- Breadth (b) = 80 cm
- Height (h) = 60 cm
The volume of the box can be calculated using the formula: Volume = l × b × h = 100 cm × 80 cm × 60 cm = 480,000 cubic centimetres (cu cm). Therefore, this box can hold 480,000 cubic centimetres, which means 480,000 unit cubes of 1 cm³ can fit inside it.
Q6. A brick is 24 cm long, 14 cm wide and 10 cm high. Find the space occupied by 500 such bricks?
Ans: Given the dimensions of the brick:
- Length (l) = 24 cm
- Width (b) = 14 cm
- Height (h) = 10 cm
The volume of one brick can be calculated using the formula: Volume = l × b × h = 24 cm × 14 cm × 10 cm = 3360 cm³. To find the space occupied by 500 such bricks, we multiply the volume of one brick by the number of bricks: Total Volume = 500 × 3360 cm³ = 1680000 cm³. Thus, the space occupied by 500 bricks is 1680000 cm³.
Q7. The volume of 6 marbles is 5 ml. Then find the volume of
(a) 24 such marbles
(b) 30 such marbles.
Ans:
Since 6 marbles have a total volume of 5 ml, we can find the volume of one marble by dividing:
Since one marble has a volume of 5/6 ml, the volume of 24 marbles is:
Similarly, for 30 marbles:
Q8. A match box measure 6 cm x 5 cm x 4 cm. Find its volume?
Ans: The volume of a matchbox can be calculated using the formula:
- Volume = length (l) × breadth (b) × height (h)
For the given matchbox dimensions:
- Length (l) = 6 cm
- Breadth (b) = 5 cm
- Height (h) = 4 cm
Substituting the values into the formula:
- Volume = 6 cm × 5 cm × 4 cm = 120 cm³
Thus, the volume of the matchbox is 120 cubic centimetres.
Q9. Find the volume of a cube whose edge is 15cm long?
Ans: The volume of a cube can be calculated using the formula:
- Volume = length × breadth × height
For a cube, all edges are equal, so we can simplify this to:
- Volume = edge × edge × edge
Given that the length of each edge is 15 cm, the calculation becomes:
- Volume = 15 cm × 15 cm × 15 cm = 3375 cm³
Therefore, the volume of the cube is 3375 cubic centimetres.
Q10. How many cubes of side 5 cm can be packed in a box of 30 cm x 25 cm x 20 cm?
Ans: To determine how many cubes with a side length of 5 cm can fit into a box with dimensions 30 cm x 25 cm x 20 cm, we first calculate the volume of the box.
- The volume of a cuboid is calculated using the formula: Volume = length x breadth x height
- Substituting the given values: Volume = 30 cm x 25 cm x 20 cm = 15000 cu cm
- Next, we calculate the volume of one cube: Volume of one cube = side x side x side = 5 cm x 5 cm x 5 cm = 125 cu cm
- To find out how many cubes can fit inside the box, we divide the volume of the box by the volume of one cube: Number of cubes = Volume of the box / Volume of one cube = 15000 cu cm / 125 cu cm = 120
- Therefore, a total of 120 cubes can be packed in the box.
The document Word Problems: How Big, How Heavy | Mathematics for Class 5: NCERT is a part of the Class 5 Course Mathematics for Class 5: NCERT.
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FAQs on Word Problems: How Big, How Heavy - Mathematics for Class 5: NCERT
| 1. What are some examples of word problems related to size and weight for Class 5 students? |  |
| 2. How can I help my child understand word problems better? | |
Ans. To help your child, encourage them to read the problem carefully, identify the key information, and visualize the scenario. Practicing with various examples and breaking down the problems into smaller, manageable parts can also be beneficial.
| 3. What strategies can be used to solve word problems about size and weight? | |
Ans. Some effective strategies include drawing diagrams, using physical objects for hands-on learning, creating equations based on the information given, and checking the work by substituting answers back into the original problem.
| 4. How do I teach my child to convert units of measurement in word problems? | |
Ans. Teach your child the basic conversion factors (e.g., 1000 grams = 1 kilogram, 100 cm = 1 meter) and practice converting units together. Provide examples where they need to convert units to solve a problem, reinforcing the concept through repetition.
| 5. Are there any online resources or worksheets for practicing word problems on size and weight? | |
Ans. Yes, there are many online resources such as educational websites that offer free worksheets and interactive games on word problems. Websites like Khan Academy, Education.com, and Math-Aids.com provide a variety of practice materials specifically for Class 5 students.
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