Question

find the curved surface area, the total surface area and volume of cylinder, the diameter of whose base is 7 cm and height being 60 cm. Also, find the capacity of the cylinder in litres​

Answer 1

Given :

• Diameter of cylinder = 7cm
• Radius of cylinder = 7/2 cm
• Height of cylinder = 60 cm

To find :

• Curved surface area
• Total surface area
• Volume
• Capacity of the cylinder in litres

Solution :

• Curved surface area of cylinder

→ 2πrh

→ 2 × 22/7 × 7/2 × 60

→ 22 × 60

→ 1320 cm²

•°• Curved surface area of cylinder = 1320cm²

_______________________________

• Total surface area of cylinder

→ 2πrh + 2πr²

→ 1320 + 2 × 22/7 × 7/2 × 7/2 [ Value of C.S.A ]

→ 1320 + 77

→ 1397 cm²

•°• Total surface area of cylinder=1397cm²

_______________________________

• Volume of cylinder

→ πr²h

→ 22/7 × 7/2 × 7/2 × 60

→ 2310 cm³

•°• Volume of cylinder = 2310 cm³

Focus Zone : 1 L = 1000 cm³

→ The capacity of the cylinder in litres

• 2310/1000 = 2.31 L

•°• The capacity of the cylinder = 2.31 L

_______________________________

Answer 2

Answer:

Given :-

• A cylinder whose diameter of a base is 7 cm and height is 60 cm.

To Find :-

• Curved surface area
• Total surface area
• Volume
• Capacity of the cylinder in litres

Formula Used :-

❶ Curved Surface Area :

✧ Curved Surface Area = 2πrh ✧

❷ Total surface area :

★ Total Surface Area = 2πr(h + r) ★

❸ Volume :

✪ Volume = πr²h ✪

Solution :-

Given :

• Diameter = 7 cm
• Radius = 7/2 = 3.5 cm
• Height = 60 cm

❶ To find curved surface area,

↦ C.S.A = 2 × 22/7 × 3.5 × 60

↦ C.S.A = 2 × 22/7 × 210

↦ C.S.A = 2 × 660

➠ C.S.A = 1320 cm²

∴ The curved surface area of a cylinder is 1320 cm² .

❷ To find total surface area,

↪ T.S.A = 2 × 22/7 × 3.5(60 + 3.5)

↪ T.S.A = 2 × 22/7 × 3.5(63.5)

↪ T.S.A = 2 × 22/7 × 222.25

↪ T.S.A = 2 × 698.5

➙ T.S.A = 1397 cm²

∴ The total surface area of a cylinder is 1397 cm² .

❸ To find volume,

⇒ Volume = 22/7 × (3.5)² × 60

⇒ Volume = 22/7 × 12.25 × 60

⇒ Volume = 22/7 × 735

➦ Volume = 2310 cm²

∴ The volume of a cylinder is 2310 cm² .

❹ To find capacity of a cylinder in litres,

We know that,

✯ 1 Litres = 1000 cm³ ✯

According to the question by using the formula we get,

↛ 1 Litre = 1000 cm²

Then,

↛ 2310/1000

➲ 2.31 L

∴ The capacity of the cylinder is 2.31 L .