Volume and surface area of Solid

2️⃣ Volume and Water Capacity

Question 2(a):
A rectangular water tank has dimensions 3 m * 2.2 m * 1.5 m. How many liters of water will it hold when filled to the brim?

Question 2(b):
A tank measures 2.5 m * 1.75 m * 1.2 m. How many liters of water does it hold when completely filled?

3️⃣ Solid and Weight

Question 3(a):
A rectangular piece of iron measures 0.95 m * 60 cm * 2 cm. If 1 cubic meter of iron weighs 7.5 tons, what is the weight of this piece in kilograms?

Question 3(b):
A piece of iron has dimensions 1.2 m * 80 cm * 1.5 cm. If 1 cubic meter of iron weighs 8 tons, what is its weight?

4️⃣ Area and Cost

Question 4(a):
The area of a courtyard is 4200 m². If it is to be covered with gravel to a height of 2 cm and gravel costs ₹7.50 per cubic meter, what is the total cost?

Question 4(b):
The area of a square yard is 3600 m². To cover it with 1.5 cm height of gravel costing ₹6 per cubic meter, what is the total expense?

5️⃣ Hall and People

Question 5(a):
A hall measures 20 m in length, 15 m in width, and 5 m in height. If 4 m³ of air is required per person, how many people can be accommodated in the hall?

Question 5(b):
A convention hall has dimensions 18 m * 12 m * 4.5 m. If 3.5 m³ of air is needed for each person, how many people can fit in the hall?

6️⃣ Box and Storage

Question 6(a):
A cardboard box is 1.5 m long, 80 cm wide, and 60 cm high. If each soap bar measures 7 cm * 5 cm * 4 cm, how many bars can the box hold?

Question 6(b):
A box measures 1.2 m * 70 cm * 50 cm. If each soap bar measures 6 cm * 4 cm * 3.5 cm, how many bars can it hold?

7️⃣ Matchbox and Packet

Question 7(a):
A matchbox measures 5 cm * 2.5 cm * 1.5 cm. If a packet contains 120 boxes, what is the total volume of the packet? How many such packets can fit in a carton of size 1.2 m * 0.8 m * 0.5 m?

Question 7(b):
A matchbox measures 4.5 cm * 2 cm * 1.5 cm. If a packet contains 144 boxes, find the total volume of the packet and how many such packets can be placed in a box of size 1.5 m * 90 cm * 0.6 m?

8️⃣ Planks from Wooden Block

Question 8(a):
How many planks of size 2 m * 25 cm * 8 cm can be prepared from a wooden block of 5 m * 70 cm * 32 cm, assuming no wastage?

Question 8(b):
A wooden block measures 6 m * 80 cm * 40 cm. How many planks of size 2.5 m * 20 cm * 10 cm can be made from it without any wastage?

9️⃣ Bricks for Wall

Question 9(a):
How many bricks of size 25 cm * 13.5 cm * 6 cm are required to build a wall 8 m long, 5.4 m high, and 33 cm thick?

Question 9(b):
A wall is 10 m long, 4.5 m high, and 30 cm thick. If each brick measures 20 cm * 10 cm * 5 cm, how many bricks are needed?

10️⃣ Bricks with Mortar

Question 10(a):
A wall 15 m long, 30 cm wide, and 4 m high is made of bricks, each measuring 22 cm * 12.5 cm * 7.5 cm. If 1/12 of the total volume is mortar, how many bricks are there in the wall?

Question 10(b):
A wall 12 m long, 25 cm thick, and 3 m high is built with bricks measuring 20 cm * 10 cm * 5 cm. If mortar takes 1/10 of the volume, find the number of bricks in the wall.

11️⃣ Cistern Capacity

Question 11(a):
Find the capacity in litres of a rectangular cistern measuring 11.2 m * 6 m * 5.8 m. Also, find the area of the iron sheet required to make it.

Question 11(b):
A cistern is 8 m long, 5 m wide, and 4 m high. Find its capacity in litres and the total iron sheet area needed.

12️⃣ Gold Sheet Thickness

Question 12(a):
A block of gold has a volume of 0.5 m³. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.

Question 12(b):
A gold block of volume 0.3 m³ is flattened to cover 0.5 hectare. Find the thickness of the sheet.

13️⃣ Rainfall Volume

Question 13(a):
If 5 cm of rainfall was recorded in a day, find the volume of water that fell on a 2-hectare field.

Question 13(b):
A field of 1.5 hectares received 6 cm of rainfall. Find the total volume of water in cubic meters.

14️⃣ River Flow Volume

Question 14(a):
A river 2 m deep and 45 m wide flows at 3 km/h. Find the quantity of water that runs into the sea per minute.

Question 14(b):
A river 3 m deep and 50 m wide flows at 4 km/h. Calculate the volume of water flowing into the sea per minute.

15️⃣ Pit Depth

Question 15(a):
A pit 5 m long and 3.5 m wide is dug. If the volume of earth taken out is 14 m³, what is the depth of the pit?

Question 15(b):
A rectangular pit 6 m long and 4 m wide is dug. If 24 m³ of earth is removed, find the depth of the pit.

16️⃣ Tank Length

Question 16(a):
A rectangular water tank is 90 cm wide and 40 cm deep. If it contains 576 litres of water, what is its length?

Question 16(b):
A tank is 1 m wide and 50 cm deep. If it can hold 750 litres of water, find its length.

17️⃣ Beam Width

Question 17(a):
A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m³ of wood. What is the width of the beam?

Question 17(b):
A wooden beam is 6 m long and 40 cm thick. If the volume of the wood is 2.4 m³, find the width of the beam.

18️⃣ Room Height

Question 18(a):
The volume of a room is 378 m³ and the area of its floor is 84 m². Find the height of the room.

Question 18(b):
A room has a floor area of 120 m² and a volume of 600 m³. Find the height of the room.

19️⃣ Swimming Pool Water Level

Question 19(a):
A swimming pool is 260 m long and 140 m wide. If 54600 m³ of water is pumped into it, find the height of the water level.

Question 19(b):
A pool is 100 m long and 50 m wide. If 15000 m³ of water is poured in, find the height of water in the pool.

20️⃣ Closed Wooden Box Volume

Question 20(a):
Find the volume of wood used to make a closed box of outer dimensions 60 cm * 45 cm * 32 cm, the thickness of wood being 2.5 cm all around.

Question 20(b):
A closed wooden box measures 80 cm * 60 cm * 40 cm externally. If the wood thickness is 3 cm, find the volume of wood used.

21️⃣ Iron Box Weight

Question 21(a):
Find the volume of iron required to make an open box whose external dimensions are 36 cm * 25 cm * 16.5 cm. The box is 1.5 cm thick throughout. If 1 cm³ of iron weighs 8.5 grams, find the weight of the empty box in kilograms.

Question 21(b):
An open iron box has external dimensions 50 cm * 40 cm * 30 cm and thickness 2 cm. If 1 cm³ of iron weighs 7.5 g, find the weight of the empty box in kilograms.

22️⃣ Box with Lid Capacity

Question 22(a):
A box with a lid is made of wood 3 cm thick. Its external length, breadth, and height are 56 cm, 39 cm, and 30 cm respectively. Find the capacity of the box and the volume of wood used.

Question 22(b):
A wooden box with a lid has external dimensions 70 cm * 50 cm * 40 cm and wood thickness 4 cm. Find the capacity of the box and the volume of wood used.

23️⃣ Closed Wooden Box Capacity

Question 23(a):
The external dimensions of a closed wooden box are 62 cm, 30 cm, and 18 cm. If the box is made of 2 cm thick wood, find the capacity of the box.

Question 23(b):
A closed wooden box has external dimensions 80 cm * 45 cm * 35 cm and wood thickness 3 cm. Find its capacity.

24️⃣ Closed Wooden Box Weight

Question 24(a):
A closed wooden box is 80 cm long, 65 cm wide, and 45 cm high. The thickness of wood is 2.5 cm. Find the capacity of the box and its weight if 100 cm³ of wood weighs 8 g.

Question 24(b):
A wooden box 100 cm * 70 cm * 50 cm is made of 3 cm thick wood. If 100 cm³ of wood weighs 9 g, find the capacity and weight of the box.

25️⃣ Cube Volume and Surface Area

Question 25(a):
Find the volume, lateral surface area, and total surface area of a cube whose edge measures 7 m.

Question 25(b):
Find the volume, lateral surface area, and total surface area of a cube whose edge measures 5.6 cm.

26️⃣ Cube Surface Area

Question 26(a):
The surface area of a cube is 1176 cm². Find its volume.

Question 26(b):
The volume of a cube is 729 cm³. Find its surface area.

27️⃣ Metal Block to Cubes

Question 27(a):
The dimensions of a metal block are 2.25 m * 1.5 m * 27 cm. It is melted and recast into cubes each of side 45 cm. How many cubes are formed?

Question 27(b):
A metal block measures 3 m * 1.8 m * 36 cm. It is recast into cubes of side 60 cm. Find the number of cubes formed.

28️⃣ Cube Edge Doubling

Question 28(a):
If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Question 28(b):
A cube has edge 5 cm. If the edge is tripled, how many times does the volume and surface area increase?

29️⃣ Cost of Cubical Block

Question 29(a):
A solid cubical block of fine wood costs ₹256 at ₹500 per m². Find its volume and the length of each side.

Question 29(b):
A cubical block costs ₹400 at ₹800 per m². Find the volume and the edge length of the cube.

2(a): 9900 लीटर

2(b): 5250 लीटर

3(a): 427.5 किलोग्राम
3(b): 768 किलोग्राम

4(a): ₹63
4(b): ₹32.4

5(a): 375 लोग
5(b): 221 लोग

6(a): 3428 बार
6(b): 6000 बार

7(a): 0.045 m³, 29 पैकेट
7(b): 0.03888 m³, 21 पैकेट

8(a): 112 प्लैंक
8(b): 96 प्लैंक

9(a): 74880 ईंटें
9(b): 67500 ईंटें

10(a): 12600 ईंटें
10(b): 5400 ईंटें

11(a): 3884160 लीटर, आयतन 389.6 m²
11(b): 1600000 लीटर, आयतन 264 m²

12(a): 0.5 मिमी
12(b): 0.6 मिमी

13(a): 1000 m³
13(b): 900 m³

14(a): 4500 m³ प्रति मिनट
14(b): 10000 m³ प्रति मिनट

15(a): 0.8 m
15(b): 1 m

16(a): 1.6 m
16(b): 1.5 m

17(a): 0.075 m
17(b): 0.1 m

18(a): 4.5 m
18(b): 5 m

19(a): 1.5 m
19(b): 3 m

20(a): 0.076 m³
20(b): 0.132 m³

21(a): 5.93 किग्रा
21(b): 12.6 किग्रा

22(a): क्षमता 0.06552 m³, लकड़ी का आयतन 0.04584 m³
22(b): क्षमता 0.112 m³, लकड़ी का आयतन 0.044 m³

23(a): 0.04752 m³
23(b): 0.0957 m³

24(a): क्षमता 0.0555 m³, वजन 44.4 किग्रा
24(b): क्षमता 0.0648 m³, वजन 58.32 किग्रा

25(a): आयतन 343 m³, पार्श्व क्षेत्रफल 294 m², कुल क्षेत्रफल 294 m²
25(b): आयतन 175.616 cm³, पार्श्व क्षेत्रफल 156.8 cm², कुल क्षेत्रफल 188.16 cm²

26(a): आयतन 512 cm³
26(b): सतह क्षेत्र 486 cm²

27(a): 16 क्यूब
27(b): 15 क्यूब

28(a): आयतन 8 गुना, सतह क्षेत्र 4 गुना
28(b): आयतन 27 गुना, सतह क्षेत्र 9 गुना

29(a): आयतन 0.064 m³, भुजा 0.4 m
29(b): आयतन 0.125 m³, भुजा 0.5 m

2. The dimensions of a rectangular water tank are

2 m 75 cm × 1 m 80 cm × 1 m 40 cm.
How many litres of water does it hold when filled to the brim?

3. A solid rectangular piece of iron measures

1.05 m × 70 cm × 1.5 cm.
Find the weight of this piece in kilograms if 1 cm³ of iron weighs 8 grams.

4. The area of a courtyard is 3750 m².

Find the cost of covering it with gravel to a height of 1 cm
if the gravel costs ₹6.40 per cubic metre.

5. How many persons can be accommodated in a hall of

length 16 m, breadth 12.5 m, height 4.5 m,
assuming that 3.6 m³ of air is required per person?

6. A cardboard box is

1.2 m long, 72 cm wide and 54 cm high.
How many bars of soap can be put into it if each soap bar measures
6 cm × 4.5 cm × 4 cm?

7. The size of a matchbox is

4 cm × 2.5 cm × 1 cm.
1️⃣ What is the volume of a packet containing 144 matchboxes?
2️⃣ How many such packets can be placed in a carton of size
1.5 m × 84 cm × 60 cm?

8. How many planks of size

2 m × 25 cm × 8 cm
can be prepared from a wooden block
5 m long, 70 cm broad and 32 cm thick
(assuming there is no wastage)?

9. How many bricks, each of size

25 cm × 13.5 cm × 6 cm,
will be required to build a wall
8 m long, 5.4 m high and 33 cm thick?

10. A wall 15 m long, 30 cm wide and 4 m high

is made of bricks each measuring
22 cm × 12.5 cm × 7.5 cm.
If 1/12 of the total volume of the wall consists of mortar,
how many bricks are there in the wall?

Hint:

Volume of bricks in the wall
= cm³

संसाधन 8th

- December 07, 2025