Given:

• Length (l) = 20 cm
• Breadth (b) = 10.5 cm
• Height (h) = 8 cm

Volume of a cuboid : = l × b × h

Substitute the given values into the formula:

∴ Volume = 20 × 10.5 × 8 = 160 × 10.5 = 1680 cm³

Answer: The volume of the box is 1680 cubic centimeters (cc or cm³).

Given Information:

• Volume = 150 cc (cubic centimeters)
• Length (l) = 10 cm
• Breadth (b) = 5 cm

The volume of a cuboid is calculated as: Volume = l × b × h

(In this problem, "thickness" refers to the height (h) of the cuboid.)

Substitute the known values into the formula:

∴ 150 = 10 × 5 × h

∴ 150 = 50 × h

∴ h = \(\frac{150}{50}\) = 3 cm

Answer: The thickness of the soap bar is 3 cm.

First convert all dimensions to centimeters (1 m = 100 cm).

For the Wall:

• Length (l1): 6 m = 600 cm
• Height (h1): 2.5 m = 250 cm
• Breadth (b1): 0.5 m = 50 cm

For one Brick:

• Length: 25 cm
• Breadth: 15 cm
• Height: 10 cm

The volume of a cuboid is calculated using: Volume = l × b × h

Volume of Wall = 600 × 50 × 250 cc

Volume of one Brick = 25 ×15 × 10 cc

Find the Number of Bricks Required :

Number of bricks = \(\frac{\text{Volume of Wall}}{\text{Volume of Brick}}\)

∴ Number of bricks = \(\frac{600 × 50 × 250}{25 ×15 × 10}\) = 40 × 50 = 2000

Answer: 2000 bricks are required to build the wall.

The tank is a cuboid with the following dimensions:

• Length (l): 10 m
• Breadth (b): 6 m
• Depth or Height (h): 3 m

Volume of a cuboid: Volume = l × b × h

Step 1: Find the capacity (volume) of the tank in cubic meters.

Capacity = 10 m × 6 m × 3 m

∴ Capacity = 180 m³

Step 2: Convert the capacity to liters.

∵ 1 m³ = 1,000 liters

To find how many liters the tank can hold, multiply the volume in cubic meters by 1,000:

∴ Liters of water = 180 × 1,000 = 180,000 liters

Answer:

• The capacity of the tank is 180 m³.
• The tank can hold 180,000 liters of water.

(1) For cylinder, radius (r) =7 cm its height (h) = 10 cm.

Curved surface area of cylinder = 2πrh

   = 2 × \(\frac{22}{7}\) × 7 × 10

   = 440 sq.cm.

Total surface area of cylinder = 2πr(r + h)

= 2 × \(\frac{22}{7}\) × 7(7 + 10)

= 44 × 17

= 748 sq.cm.

Answer :

• Curved surface area of cylinder is 440 sq cm
• Total surface area of cylinder is 748 sq cm.

(2) For cylinder, radius (r) = 1.4 cm its height (h) = 2.1 cm.

Curved surface area of cylinder = 2πrh

   = 2 × \(\frac{22}{7}\) × 1.4 × 2.1

   = 44 × 0.2 × 2.1 = 18.48 sq.cm.

Total surface area of cylinder = 2πr(r +h)

= 2 × \(\frac{22}{7}\) × 1.4(1.4 + 2.1)

= 44 × 0.2(3.5) = 44 × 0.7

= 30.8 sq.cm.

Answer :

• Curved surface area of cylinder is48 sq cm
• Total surface area of cylinder is8 sq cm.

(3) For cylinder, r = 2.5 cm,h = 7 cm

CSA = 2 × \(\frac{22}{7}\) ​× 2.5 × 7 = 44 × 2.5 = 110 sq cm.

TSA = 2 × \(\frac{22}{7}\)​ × 2.5 × (7 + 2.5) =  × 9.5 ≈ 149.29 sq cm.

Answer :

• Curved surface area of cylinder is 110 sq cm
• Total surface area of cylinder is29 sq cm.

(4) For cylinder, r = 70 cm, h = 1.4 cm

CSA = 2  × ​\(\frac{22}{7}\) × 70 × 1.4 = 440 × 1.4 = 616 sq cm.

TSA = 2 × ​\(\frac{22}{7}\) × 70 × (1.4 + 70) = 440 × 71.4 = 31,416 sq cm.

Answer :

• Curved surface area of cylinder is 616 sq cm
• Total surface area of cylinder is 31416 sq cm.

 (5) For cylinder, r = 4.2 cm, h = 14 cm

CSA = 2 × \(\frac{22}{7}\)​ × 4.2 × 14 = 44 × 0.6 × 14 = 369.60 sq cm.

TSA = 2 × \(\frac{22}{7}\) ​× 4.2 × (14 + 4.2) = 44 × 0.6 × 18.2 = 480.48 sq cm.

Answer :

• Curved surface area of cylinder is60 sq cm
• Total surface area of cylinder is48 sq cm.

Given :

• Diameter (d): 50 cm, ∴ r = 50/2 = 25 cm
• Height (h): 45 cm
• Value of π : 3.14

Total Surface Area (TSA) of a closed cylinder is: TSA = 2πr(r +h)

∴ TSA = 2 × 3.14 × 25 × (45 + 25)

= 2 × 3.14 × 25 × 70

= 50 × 3.14 × 70

= 10,990

Answer:

The total surface area of the closed cylindrical drum is 10,990 sq cm.

Given :

• Curved Surface Area (CSA): 660 sq cm
• Height (h): 21 cm
• π: \(\frac{22}{7}\)

Find the Radius (r) :

Curved Surface Area of a cylinder = 2πrh

substitute the known values:

660 = 2 × \(\frac{22}{7}\) × r × 21

660 = 2 × 22 × r × 3

660 = 132 × r

r = \(\frac{660}{132}\)  = 5  cm

Find the Area of the Base :

Area of base = πr² = \(\frac{22}{7}\) × 5² = \(\frac{22}{7}\) × 25 = 78.50 sq cm

Answer:

• The radius of the cylinder is 5 cm.
• The area of the base of the cylinder is 78.50 sq cm.

The container is a cylinder open at the top, meaning it consists of the curved surface area and only one circular base.

Given:

Diameter (d): 28 cm

Height (h): 20 cm

Radius (r): 28/2 = 14 cm

Curved Surface Area (CSA): 2πrh

CSA = 2 × \(\frac{22}{7}\) × 14 × 20

= 2 × 22 × 2 × 20 = 1760  sq cm

Area of the Base: πr²

Base Area = \(\frac{22}{7}\) × 14 × 14

= 22 × 2 × 14 = 616 sq cm

Total Area for Container: 1760 + 616 = 2376 sq cm

Area of the sheet for the lid :

The lid is also a cylinder open at one side (the bottom), with its own height.

Given:

Radius (r): 14 cm (same as the container)

Height of lid (h_lid): 2 cm

Curved Surface Area of Lid: 2πrh_lid

CSA_lid = 2 × \(\frac{22}{7}\) × 14 × 2

= 2 × 22 × 2 × 2 = 176 sq cm

Area of the Top Face: 616 sq cm (same as the base area calculated above)

Total Area for Lid: $176 + 616 = 792 sq cm

Answer:

The area of the sheet required for the container is 2376 sq cm.

The approximate area of the sheet required for the lid is 792 sq cm.

The volume of a cylinder is calculated by multiplying the area of its circular base by its height:

Volume of a cylinder = πr²h (For these calculations, we use π = ).

(1) r = 10.5 cm, h = 8 cm

Substitute the values: Volume = \(\frac{22}{7}\) × (10.5)² × 8

  = \(\frac{22}{7}\) × 110.25 × 8

  = \(\frac{22}{7}\) × 882 = 22 × 126 = 2772 cm³

Answer: 2772 c cm.

(2) r = 2.5 m, h = 7 m

Substitute the values: Volume = \(\frac{22}{7}\) × (2.5)² × 7

  = 22 × 6.25 = 137.5 m³

Answer: 137.5 c m (cubic meters).

(3) r = 4.2 cm, h = 5 cm

Substitute the values: Volume = \(\frac{22}{7}\) × (4.2)² × 5

  = \(\frac{22}{7}\) × 17.64 × 5

  = 22 × 2.52 × 5

  = 22 × 12.6 = 277.2 cm³

Answer: 277.2 c cm.

(4) r = 5.6 cm, h = 5 cm

Substitute the values: Volume = \(\frac{22}{7}\) × (5.6)² × 5

  = \(\frac{22}{7}\) × 31.36 × 5

  = 22 × 4.48 × 5

  = 22 × 22.4 = 492.8 cm³

Answer: 492.8 c cm.

Need to calculate the volume of a cylindrical iron rod.

The rod is a cylinder with the following dimensions:

• Length (Height, h): 90 cm.
• Diameter (d): 1.4 cm.
• Radius (r) = 1.4/2 = 0.7 cm

The volume of a cylinder is calculated as: Volume = πr²h

Substitute the values: Volume = \(\frac{22}{7}\) × (0.7)² × 90

  = \(\frac{22}{7}\) × 0.49 × 90

  = 22 × 0.07 × 90

  = 138.6 cm³

Answer:

138.6 c cm (cubic centimeters) of iron is needed to make the rod.

Interior diameter of the tank = 1.6 m

its radius (r) = 0.8 m

its depth (h) = 0.7 m

Volume of the tank = πr²h

Substitute the values: Volume = \(\frac{22}{7}\) × (0.8)² × 0.7

  = 22 × 0.8 × 0.8 × 0.1 = 1.408 m³

  = 1408 litres.    ….(∵ 1m³ = 1000 litres)

Answer : Tank can hold 1408 litres of water.

Circumference of the base of the cylinder = 132 cm

its height (h) = 25 cm

Circumference of the base of the cylinder = 2πr

∴ 132 = 2 × \(\frac{22}{7}\) × r

∴ r = \(\frac{132×7}{22×2}\)

∴ r = 3 x 7

∴ r = 21 cm

Volume of the cylinder = πr²h

= \(\frac{22}{7}\) × (21)² × 25

= 22 × 3 × 21 × 25 = 34650 cu cm

Answer : Volume of the cylinder is 34650 cu cm.