CBSE Class 5 Mathematics Volume And Nets Worksheet Set 01

Question 5. The breadth of a garden is 8.7 m and its length is 15.3 m. What is the perimeter of the garden?
Answer: Length (\(l\)) = 15.3 m
Breadth (\(b\)) = 8.7 m
Perimeter of a rectangle = \(2 \times (l + b)\)
\(\text{Perimeter} = 2 \times (15.3 + 8.7)\)
\(\text{Perimeter} = 2 \times 24.0 = 48.0\text{ m}\)
In simple words: The perimeter is the total distance around the garden, found by adding length and breadth together and multiplying by 2.

Exam Tip: Always write the formula first before substituting values to secure full marks.

Unit 10 - Volume and Nets

I Fill in the blanks

Question 1. The volume of an object is the amount of space it occupies.
Answer: volume
In simple words: Volume measures how much three-dimensional space a solid object takes up.

Exam Tip: Remember that 'space occupied' is the core definition of volume.

Question 2. The volume of an object is the amount of space it occupies.
Answer: space
In simple words: The amount of space taken up by an object is called its volume.

Exam Tip: Keep the definition concise and accurate.

Question 3. Volume of a cube of side 1 mm is
Answer: 1 cubic mm (or \(1\text{ mm}^3\))
In simple words: Volume of a cube is side multiplied by side multiplied by side, so \(1 \times 1 \times 1 = 1\text{ mm}^3\).

Question 4. The unit of measurement of volumes is
Answer: cubic units (or cu. units / \(\text{cm}^3\), \(\text{m}^3\), etc.)
In simple words: Volume is always measured in cubic units because it involves three dimensions (length, breadth, height).

Exam Tip: Always specify the unit as cubic units or use the power of 3.

Question 5. A cubic millimeter (\(\text{mm}^3\)) is used to measure the volume of very small objects.
Answer: cubic millimeter (or cu. mm)
In simple words: Tiny objects are measured using very small units like cubic millimeters.

Exam Tip: Match the unit size to the scale of the object being measured.

Question 6. A cubic meter (\(\text{m}^3\)) is used to measure the volume of large objects.
Answer: cubic meter (or cu. m)
In simple words: Large spaces and objects are measured in cubic meters.

Exam Tip: Large dimensions use meters, so large volumes use cubic meters.

Question 7. Volume of a cuboid of length 'l', breadth 'b' and height 'h' is
Answer: \(l \times b \times h\)
In simple words: Multiply length, breadth, and height to find a cuboid's volume.

Exam Tip: Memorize the standard cuboid volume formula.

Question 8. Volume of a cuboid of length 3 cm, breadth 2 cm and height 1 cm is
Answer: \(3\text{ cm} \times 2\text{ cm} \times 1\text{ cm} = 6\text{ cu. cm}\)
In simple words: Multiply 3, 2, and 1 to get 6 cubic centimeters.

Exam Tip: Always write the unit as cu. cm or \(\text{cm}^3\).

Question 9. \(V = l \times b \times \text{____}\)
Answer: \(h\)
In simple words: Volume equals length times breadth times height.

Exam Tip: Understand how the formula variables relate to each other.

Question 10. \(\text{____} = \frac{V}{b \times h}\)
Answer: \(l\)
In simple words: Length is calculated by dividing volume by the product of breadth and height.

Exam Tip: Use transposing rules of equations to find missing dimensions.

Question 11. \(h = \frac{V}{\text{____}}\)
Answer: \(l \times b\)
In simple words: Height is volume divided by length times breadth.

Exam Tip: The denominator represents the base area of the cuboid.

Question 12. \(\text{____} = \frac{V}{l \times h}\)
Answer: \(b\)
In simple words: Breadth is found by dividing volume by length times height.

Exam Tip: Breadth is missing here, so it is isolated on the left side.

Question 13. Volume of a cube is measured in cubic units.
Answer: cubic
In simple words: Cube volume uses cubic units of length.

Exam Tip: All volume measurements require cubic units.

II Do the following

Question 1. Find the volume of each of the following
a) \(l = 5\text{ mm}, b = 12\text{ mm}, h = 9\text{ mm}\)
Answer: Volume = \(l \times b \times h\)
\(V = 5 \times 12 \times 9\)
\(V = 60 \times 9 = 540\text{ cu. mm}\)
In simple words: Multiply 5, 12, and 9 to get 540 cubic millimeters.

Exam Tip: Multiply numbers step by step to avoid calculation errors.

Question 1.
b) \(l = 21\text{ cm}, b = 8\text{ cm}, h = 12\text{ cm}\)
Answer: Volume = \(l \times b \times h\)
\(V = 21 \times 8 \times 12\)
\(V = 168 \times 12 = 2016\text{ cu. cm}\)
In simple words: Multiply 21 by 8, then multiply the result by 12.

Exam Tip: Double-check multiplication involving two-digit numbers.

Question 1.
c) \(l = 5\text{ m}, b = 3\text{ m}, h = 30\text{ m}\)
Answer: Volume = \(l \times b \times h\)
\(V = 5 \times 3 \times 30\)
\(V = 15 \times 30 = 450\text{ cu. m}\)
In simple words: Multiply 5, 3, and 30 to get 450 cubic meters.

Exam Tip: Ensure the unit matches the dimensions given in meters.

Question 2. Find the missing side.
a) \(l = 5\text{ m}, b = 7\text{ m}, V = 350\text{ cu. m}, h = ?\)
Answer: \(h = \frac{V}{l \times b}\)
\(h = \frac{350}{5 \times 7}\)
\(h = \frac{350}{35} = 10\text{ m}\)
In simple words: Divide the total volume by the product of length and breadth to find height.

Exam Tip: Write the rearranged formula clearly before dividing.

Question 2.
b) \(b = 12\text{ cm}, h = 8\text{ cm}, V = 1056\text{ cu. cm}, l = ?\)
Answer: \(l = \frac{V}{b \times h}\)
\(l = \frac{1056}{12 \times 8}\)
\(l = \frac{1056}{96} = 11\text{ cm}\)
In simple words: Divide total volume by breadth times height to find length.

Exam Tip: Perform long division carefully when simplifying fractions.

Question 2.
c) \(l = 6\text{ mm}, h = 6\text{ mm}, V = 3600\text{ cu. mm}, b = ?\)
Answer: \(b = \frac{V}{l \times h}\)
\(b = \frac{3600}{6 \times 6}\)
\(b = \frac{3600}{36} = 100\text{ mm}\)
In simple words: Divide 3600 by 36 to get 100 millimeters.

Exam Tip: Simplify the denominator first before performing division.

Question 3. Do as directed.
1. A rectangular box is 35 cm long, 10 cm height and 35 cm wide. What is the volume of the rectangular box?
Answer: Length (\(l\)) = 35 cm
Height (\(h\)) = 10 cm
Breadth / Width (\(b\)) = 35 cm
Volume = \(l \times b \times h\)
\(V = 35 \times 35 \times 10\)
\(35 \times 35 = 1225\)
\(V = 1225 \times 10 = 12250\text{ cu. cm}\)
In simple words: Multiply length, width, and height to find the total volume of the box.

Exam Tip: 'Wide' and 'breadth' mean the same thing in geometry problems.

Question 3.
2. A brick has a length of 19 cm, breadth of 7 cm, and height of 6 cm. What will be the volume of 20 such bricks?
Answer: Length of one brick (\(l\)) = 19 cm
Breadth of one brick (\(b\)) = 7 cm
Height of one brick (\(h\)) = 6 cm
Volume of one brick = \(19 \times 7 \times 6\)
\(19 \times 7 = 133\)
\(133 \times 6 = 798\text{ cu. cm}\)
Volume of 20 bricks = \(798 \times 20 = 15960\text{ cu. cm}\)
In simple words: Find the volume of one brick, then multiply by 20 to find the total volume.

Exam Tip: Always calculate the volume of a single item first before multiplying by the total count.

Fill in the blanks

Question 1. If we place an object of volume 20 cu. cm in a measuring glass, the water level will rise by ____ ml.
Answer: 20
In simple words: An object submerged in water displaces a volume of water equal to its own volume (\(1\text{ cu. cm} = 1\text{ ml}\)).

Exam Tip: Remember the conversion: 1 cubic centimeter equals 1 milliliter of water.

Question 2. ____ cu. cm is the volume of an object that makes the level of water rise by 10 ml.
Answer: 10
In simple words: A rise of 10 ml in water level means the submerged object has a volume of 10 cubic centimeters.

Exam Tip: Water displacement is directly proportional to the volume of the object.

Question 3. A cuboid of volume ____ cu. cm occupies the same space as 60 ml of water.
Answer: 60
In simple words: Since 60 ml equals 60 cubic centimeters, the cuboid's volume must be 60 cu. cm.

Exam Tip: 1 ml equals 1 cu. cm, so numerical values remain the same during conversion.

Question 2. Measure these angles with a protractor. Then state what type of angles they are.
Answer: 1. First angle (top-left): Measures \(120^\circ\) - Obtuse angle.
2. Second angle (top-right): Measures \(90^\circ\) - Right angle.
3. Third angle (bottom): Measures \(110^\circ\) - Obtuse angle.
In simple words: Use a protractor to measure degrees. Angles less than \(90^\circ\) are acute, exactly \(90^\circ\) are right, and between \(90^\circ\) and \(180^\circ\) are obtuse.

Exam Tip: Align the center of the protractor precisely with the vertex of the angle to read the correct measurement.