Question

The radius and the height of
Cylinder are in the ratio 7:3.
$if \: the \: volume \: of \: cylinder \:$
$is \: {12474cm}^{3}$

Find the curved surface area and total surface area of cylinder.

Answer 1

Answer:

(i) Curved surface area = 1188 cm²

(ii) Total surface area = 3960 cm²

Step-by-step explanation:

Given that radius and height are in the ratio of 7:3.

Let us consider the radius and height as 7x and 3x respectively.

Given volume of cylinder = 12474 cm³.

⇒ πr²h = 12474

⇒ π(7x)² * 3x = 12474

⇒ (22/7) * 49x² * 3x = 12474

⇒ 22 * 21x³ = 12474

⇒ x³ = 27

⇒ x = 3

Hence,

∴ Radius of the cylinder = 21  cm.

∴ Height of the cylinder = 9 cm.

(i)

Curved surface area of the cylinder = 2πrh

⇒ 2 * (22/7) * (21) * 9

⇒ 1188 cm²

(ii)

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

⇒ 2 * (22/7) * 21(21 + 9)

⇒ 2 * 22 * 3(30)

⇒ 3960 cm²

Hope it helps!

Answer 2

Step-by-step explanation:

radius and height are 7x and 3x.

volume of cylinder = 12474 cm³.

πr²h = 12474

π(7x)² * 3x = 12474

(22/7) * 49x² * 3x = 12474

22 * 21x³ = 12474

x³ = 27

x = 3

Radius of the cylinder = 21  cm.

Height of the cylinder = 9 cm.

Curved surface area of the cylinder = 2πrh

2 * (22/7) * (21) * 9

1188 cm²

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

2 * (22/7) * 21(21 + 9)

2 * 22 * 3(30)

3960 cm²