Question

The radius and height of a cylinder are in the ratio 2:3. If the curved surface area of the cylinder is 1848 sq.cm, find its radius, height and the total surface area.​

Answer 1

Step-by-step explanation:

The radius and height of a cylinder are in the ratio 2:3

Let the radius, r = 2x

           height, h = 3x

$\text{Given that the curved surface area of the cylinder =} 1848\ cm^2\\ \\ \Rightarrow 2 \pi rh=1848\\ \\ \Rightarrow 2 \times \frac{22}{7} \times 2x \times 3x=1848\\ \\ \Rightarrow x^2=\frac{1848 \times 7}{2 \times 22 \times 2 \times 3}\\ \\ \Rightarrow x^2=49\\ \\ \Rightarrow x=\sqrt{49} = 7$

Thus, Radius = 2x = 2×7 = 14 cm

Height = 3x = 3×7 = 21 cm

Total Surface area = 2πr(r+h) = 2 × 22/7 × 14 (14+21) = 3080 cm²

Answer 2

GIVEN :-

• radius and height of a cylinder are in the ratio 2:3. If the curved surface area of the cylinder is 1848 sq.cm

TO FIND :-

• find its radius, height and the total surface area = ?

SOLUTION :-

• Let radius of the cylinder be 2x and height of the cylinder be 3x

• Volume = 1848 cm³

• πr²h = 1848

• 22/7 × (2x) × 3x = 1848
• 22/7 × 4x² × 3x = 1848

• x = 1848 × 7/22 × 12 = 49

• x = 7

so, r = 2 × 7 = 14 cm

h = 3 × 7 = 21 cm

now ,the total surface area.

= 2 × 22/7 × 14 ( 14 +21)

2 × 22 × 2 × 35 = 3080 cm^2