Question

find ratio between total surface area and curved surface area of a cylinder with height = 7.5m radius = 3.5m​

Answer 1

Answer:

Ratio is 22:15 .

Step-by-step explanation:

Given :

• Height of cylinder is 7.5 m.
• Radius of cylinder is 3.5 m.

To find :

• Ratio between total surface area and curved surface area of the cylinder.

Solution :

We know,

Total surface area of cylinder = 2πr² + 2πrh

[Where, r is radius and h is height of cylinder]

Put r and h in formula :

$\implies$ 2 × 22/7 × (3.5)² + 2 × 22/7 × (3.5) × (7.5)

$\implies$ 44/7 × 12.25 + 44/7 × 26.25

$\implies$ 539/7 + 1155/7

$\implies$ 1694/7

$\implies$ 242

Total surface area is 242 m².

And we also know that,

Curved surface area of cylinder = 2πrh

Put all values :

$\implies$ 2 × 22/7 × (3.5) × (7.5)

$\implies$ 44/7 × 26.25

$\implies$ 1155/7

$\implies$ 165

Curved surface area is 165 m².

Now,

Ratio = Total surface area/Curved surface area

$\implies$ 242/165

$\implies$ 22/15

Therefore,

Ratio of total surface area and curved surface area is 22 : 15 .

Answer 2

Height of cylinder = h = 7.5 m

Radius of cylinder = r = 3.5 m

Total surface area of cylinder = 2πr² + 2πrh

TSA =  [2 × 3.14 × (3.5)²] + [2 × 3.14 × (3.5) × (7.5)]

=> TSA = 242

Total surface area = 242 m².

We know,

Curved surface area of cylinder = 2πrh

=>CSA = 2 × 3.14 × (3.5) × (7.5)

=> CSA= 165

Curved surface area is 165 m².

Hence,

Required Ratio = Total surface area/Curved surface area

= 242/165

= 22/15