CBSE Class 8 Mathematics Mensuration Assignment Set 04

Question. Three cubes of iron with sides 3 cm, 4 cm and 5 cm are melted to form a new cube.
What is the side of the new cube?
Answer : 6 cm

Question. Two cylinder have sam e base radiu s r. If their heights are 5 cm and 15 cm. What is the ratio of their volumes?
Answer : 1:3

Question. If base radius of a cylinder is doubled then the volume of new cylinder = ______ times the volume of given cylinder.
Answer : 4

Question. Capacity of cylindrical tank is 1 m³. How much litre water it can contain?
Answer : 1000 litre

Question. A small cube of side 4 cm is placed in a cube of side 5cm. Find the volume of the air in between the two cubes.
Answer : 61 cm³

Question. Find the side of a cube whose total surface area is 600 cm².
Answer : 10 cm

Question. If the volume of a right circular cylinder, 3 cm high is 462 cm³. What is the radius of the base of cylinder?
Answer : 7 cm

Question. Find the volume of cube whose side is 0.4 cm.
Answer : 0.064 cm³

Question. What is the area of triangle whose base is 36 cm and height is 7 cm?
Answer : 126 cm²

Question. Lateral surface area of a cube is 100m². What is the length of its edge?
Answer : 5 m

Question. If the edges of a room are in the ratio 3:2:1 and its total surface area is 198 m². What is the length of the room?
Answer : 9 m

Question. The sides of a room are in the ratio 5:3:2. If the volume of the room is 3750 cubic meters. Find the length of the room.
Answer : 25 m

Question. The area of rhombus is 120 cm² and one diagonal is 5 cm. Find the length of other diagonal.
Answer : 48 cm

Questions carrying 1 Mark each :-

Q.1 Write the formula to find the area of a parallelogram.

Q.2 Find the lateral surface area of a cube of edge a cm.

Q.3 1 Litre = _______ 1 ³ .

Question carrying 2 marks each:-

Q.4 The parallel sides of a trapezium are 12 m. and 8 m. and the distance between them is 6m. Find the area of the trapizium.

Q.5 A cuboidal wooden block contains 144 cu cm. of wood. If it is 6 cm. long and 3 cm. wide, find its height.

Q.6 The height of a cylinder is 15 cm. and curved surface area is 660 ÿ 0 ² . Find the radius of the cylinder.

Q.7 The total surface area of a cube is 96m2. Find its volume.

Q.8 The diagonals of a rhombus are of length 16 cm. and 30 cm. Find its area.

Questions carrying 3 marks each:-

Q.9 Find the area of the quadrilateral shown in figure:

Q.10 The area of a trapezium is 0² and the distance between the parallel sides is ÿÿ. Find the length of the parallel sides if they are in the ratio 3:4.

Q.11 Three cubes, each of edge 2 cm. long are placed together. Find the total surface area of the cuboid so formed.

Q.12 The rainfall on a certain day was 12 cm. How many liters of water fell on 3 hectares of land on that day?

Q.13 The daimeter of a road roller, 1m40cm long is 80cm. If it takes 600 revolutions to level a playground, find the cost of levelling the ground at Rs. 3 perm2.

Questions carrying 6 marks each:

Q.14 A rectangular sheet of aluminium foil is 44 cm. long and 20 cm. wide. A cylinder is made out of it, by rolling the foil along width. Find the volume of the cylinder.

Q.15 The perimeter of the floor of a hall is 250 m. If the height is 4 m, find the cost of painting the four walls at the rate of Rs. 12 per square meter.

Q.16 BY how many times do the volume and surface area of a cube increase if its edges get doubled.

Multiple choice Questions carrying 1 marks each:-

Q.17 If the edges of a cube are halved, then its volume become:
(a) 4 times
(b) 8 times
(c) 1/8 times
(d) 0/2 times

Q.18 The lateral surface area of a cylinder is
(a) 2 ²h
(b) ππrh
(c) 222(2)h) 
(d) none of these.

Questions carrying 1 Mark each :-

Q.1 Write the formula to find the area of a parallelogram.

Q.2 Find the lateral surface area of a cube of edge a cm.

Q.3 1 Litre = _______ 1 ³

Question carrying 2 marks each:-

Q.4 The parallel sides of a trapezium are 12 m. and 8 m. and the distance between them is 6m. Find the area of the trapizium.

Q.5 A cuboidal wooden block contains 144 cu cm. of wood. If it is 6 cm. long and 3 cm. wide, find its height.

Q.6 The height of a cylinder is 15 cm. and curved surface area is 660 0 ² . Find the radius of the cylinder.

Q.7 The total surface area of a cube is 96m2. Find its volume.

Q.8 The diagonals of a rhombus are of length 16 cm. and 30 cm. Find its area.

Questions carrying 3 marks each:-

Q.9 Find the area of the quadrilateral shown in figure:

Q.10 The area of a trapezium is 0² and the distance between the parallel sides is ÿÿ. Find the length of the parallel sides if they are in the ratio 3:4.

Q.11 Three cubes, each of edge 2 cm. long are placed together. Find the total surface area of the cuboid so formed.

Q.12 The rainfall on a certain day was 12 cm. How many liters of water fell on 3 hectares of land on that day?

Q.13 The daimeter of a road roller, 1m40cm long is 80cm. If it takes 600 revolutions to level a playground, find the cost of levelling the ground at Rs. 3 perm2.

Questions carrying 6 marks each:

Q.14 A rectangular sheet of aluminium foil is 44 cm. long and 20 cm. wide. A cylinder is made out of it, by rolling the foil along width. Find the volume of the cylinder.

Q.15 The perimeter of the floor of a hall is 250 m. If the height is 4 m, find the cost of painting the four walls at the rate of Rs. 12 per square meter.

Q.16 BY how many times do the volume and surface area of a cube increase if its edges get doubled.

Multiple choice Questions carrying 1 marks each:-

Q.17 If the edges of a cube are halved, then its volume become:
(a) 4 times
(b) 8 times
(c) 1/8 times
(d) 0/2 times

Q.18 The lateral surface area of a cylinder is
(a) 2 ²h
(b) ππrh
(c) 222(2)h) 
(d) none of these.

M.C.Q.

Question 1. The volume of a cylinder of radius 5cm and height 7cm is
(a) \( 550\text{ cm}^2 \)
(b) \( 450\text{ cm}^2 \)
(c) \( 600\text{ cm}^2 \)
(d) \( 457\text{ cm}^2 \)
Answer: (a) \( 550\text{ cm}^2 \)
In simple words: Use the formula \( \pi r^2 h \). Multiply \( \frac{22}{7} \times 5 \times 5 \times 7 \) to get 550.

Exam Tip: Remember to square only the radius, not the height, when finding the volume of a cylinder.

Question 2. A Cylindrical tank has a capacity of 6160 cu.cm. If the diameter is 28cm, the depth of tank is
(a) 20cm
(b) 10cm
(c) 15cm
(d) 10.5cm
Answer: (b) 10cm
In simple words: First divide the diameter by 2 to get a radius of 14 cm. Then divide the volume by \( \pi r^2 \) to find the depth of 10 cm.

Exam Tip: Always convert diameter to radius before using the cylinder volume formula - forgetting to halve the diameter is the most common mistake.

Question 3. Two right circular cylinders of equal volume are such that their radii are in the ratio 2:3 . The ratio of their heights will be,
(a) 2:3
(b) 3:2
(c) 9:4
(d) 4:9
Answer: (c) 9:4
In simple words: When volumes match, the heights are inversely proportional to the square of their radii. Square 3 and 2 to get 9:4.

Exam Tip: When two cylinders have equal volumes, the ratio of their heights is the inverse square of their radii ratio: \( \frac{h_1}{h_2} = \left(\frac{r_2}{r_1}\right)^2 \).

Question 4. Area of a regular hexagon of side 4cm is
(a) \( \frac{\sqrt{3}}{4}\text{ cm}^2 \)
(b) \( 12\sqrt{3}\text{ cm}^2 \)
(c) \( \frac{\sqrt{3}}{12}\text{ cm}^2 \)
(d) \( 24\sqrt{3}\text{ cm}^2 \)
Answer: (d) \( 24\sqrt{3}\text{ cm}^2 \)
In simple words: A regular hexagon is made of 6 equilateral triangles. Multiply 6 by \( \frac{\sqrt{3}}{4} \times 4^2 \) to get \( 24\sqrt{3}\text{ cm}^2 \).

Exam Tip: Always recall that the area of a regular hexagon with side \( a \) is \( 6 \times \frac{\sqrt{3}}{4} a^2 \).

Question 5. If V is the volume and C is the curved surface of cylinder with radius r, then
(a) \( 2V = Cr \)
(b) \( V = Cr \)
(c) \( C = Vr \)
(d) \( r = VC \)
Answer: (a) \( 2V = Cr \)
In simple words: Volume is \( \pi r^2 h \) and curved surface is \( 2\pi r h \). Dividing volume by curved surface gives \( \frac{r}{2} \), which means \( 2V = Cr \).

Exam Tip: Set up a ratio of the two standard formulas \( \frac{V}{C} = \frac{\pi r^2 h}{2\pi rh} \) to cancel out \( \pi \) and \( h \) quickly.

Question 6. The capacity of a closed cylinder is 141 3/7 cm³. and radius 3cm, its height is
(a) 4cm
(b) 5cm
(c) 6cm
(d) 3cm
Answer: (b) 5cm
In simple words: Turn the mixed fraction into \( \frac{990}{7}\text{ cm}^3 \). Divide this volume by \( \pi r^2 \) to get 5 cm.

Exam Tip: Convert mixed numbers into improper fractions first before simplifying with \( \pi = \frac{22}{7} \).

Question 7. The diameter of a roller is 3.5cm and its height is 1m. its volume in cm³ is
(a) \( 3580\text{ cm}^3 \)
(b) \( 3085\text{ cm}^3 \)
(c) \( 3850\text{ cm}^3 \)
(d) \( 3000\text{ cm}^3 \)
Answer: (c) \( 3850\text{ cm}^3 \)
In simple words: Convert the 1 m height into 100 cm. Using the cylinder volume formula gives \( 3850\text{ cm}^3 \).

Exam Tip: Make sure all dimensions are in the same unit before calculating - convert meters to centimeters first.

Question 8. The volume of 1m long circular iron rod is 3850 cm³. Its diameter is
(a) 7.5cm
(b) 6.5cm
(c) 5.5cm
(d) 7cm
Answer: (d) 7cm
In simple words: Change 1 m to 100 cm. Solve for radius squared to find \( r = 3.5\text{ cm} \), then double it to get a diameter of 7 cm.

Exam Tip: The question asks for the diameter, so double the radius at the end to avoid losing full marks.

Question 9. A closed cylindrical tank of radius 7m and height 7m is made from a sheet. How much sheet is required?
(a) \( 616\text{ m}^2 \)
(b) \( 661\text{ m}^2 \)
(c) \( 166\text{ m}^2 \)
(d) \( 666\text{ m}^2 \)
Answer: (a) \( 616\text{ m}^2 \)
In simple words: A closed tank needs sheet for the curved side and both flat ends. Use total surface area \( 2\pi r(r + h) \) to find \( 616\text{ m}^2 \).

Exam Tip: For a closed cylinder, always calculate total surface area \( 2\pi r(r + h) \), not just curved surface area.

Question 10. A road roller takes 500 complete revolutions to level a field. Find the area of the field if the radius of the roller is 35cm and its height is 0.5m, the area in m² is
(a) \( 555\text{ m}^2 \)
(b) \( 550\text{ m}^2 \)
(c) \( 552\text{ m}^2 \)
(d) \( 255\text{ m}^2 \)
Answer: (b) \( 550\text{ m}^2 \)
In simple words: One turn covers the curved surface area, which is \( 1.1\text{ m}^2 \). Multiply by 500 turns to find the full field area of \( 550\text{ m}^2 \).

Exam Tip: Area leveled in one revolution equals the curved surface area (\( 2\pi rh \)) - do not include base areas.