Question

The volume of a cylinder of height 8 cm is 1232 cm2 . Find its lateral surface area and Total surface area.

Answer 1

Given :-

• Volume of cylinder = 1232 cm³
• Height = 8 cm

To find :-

• LSA & TSA of cylinder = ?

Solution :-

Here, we know,

→ Volume of cylinder = πr²h

Putting all values :-

→ 1232 = 22/7 × r² × 8

→ 1232 = 176r²/7

→ 176r² = 1232 × 7

→ 176r² = 8624

→ r² = 8624/176

→ r² = 49

→ r = √49

→ r = 7 cm

So, radius of cylinder = 7 cm

Now, ur solutions :-

i) We know,

→ LSA of cylinder = 2πrh

Putting all values

→ LSA = 2 × 22/7 × 7 × 8

→ LSA = 2 × 22 × 8

→ LSA = 352 cm²

∴ LSA of cylinder = 352 cm²

$\rule{200}{1}$

ii) We know,

→ TSA of cylinder = 2πr(r + h)

Putting all values

→ TSA = 2 × 22/7 × 7(7 + 8)

→ TSA = 2 × 22(15)

→ TSA = 2 × 22 × 15

→ TSA = 660 cm²

∴ TSA of cylinder = 660 cm²

Answer 2

Given :-

• Volume of Cylinder = 1232cm³.
• Height of Cylinder = 8cm.

To Find :-

• CSA & TSA of Cylinder ?

Formula used :-

• Lateral surface area = Curved surface Area = CSA = 2 * π * Radius * Height .
• Total surface area = TSA = CSA + 2 Base Area = CSA + 2 * π * (Radius)² .

Solution :-

Putting Values in Volume formula we get :-

➻ π * r² * h = 1232

➻ (22/7) * r² * 8 = 1232

➻ r² = (1232 * 7) / (22 * 8)

➻ r² = (112 * 7) / (2 * 8)

➻ r² = (784/16)

➻ r² = (28 * 28) / (4 * 4)

➻ r² = 7 * 7

➻ r = 7cm.

Putting This Value in CSA formula Now :-

➺ CSA = 2 * π * r * h

➺ CSA = 2 * (22/7) * 7 * 8

➺ CSA = 44 * 8

➺ CSA = 352cm². (Ans). ------ Equation ❶

Putting Value of Equation ❶ In TSA formula Now :-

➼ TSA = CSA + 2πr²

➼ TSA = 352 + [ 2 * (22/7) * (7)²

➼ TSA = 352 + [ 2 * 22 * 7 ]

➼ TSA = 352 + 308

➼ TSA = 660cm². (Ans).

∴ Lateral Surface Area of Cylinder is 352cm² & Total Surface Area of Cylinder is 660cm².