Question

The radius and height of a cylinder are in the ratio 5 : 7 and its curved surface area is 220 cm² Find its radius and height...,..............................................................plz answer step by step full solution dont spam​

Answer 1

${\huge{\rm{\underline{\underline{Question:-}}}}}$

The radius and height of a cylinder are in the ratio 5 : 7 and its curved surface area is 220 cm² Find its radius and height.

${\huge{\rm{\underline{\underline{Given:-}}}}}$

⇒ Ratio of radius and height = 5 : 7

⇒ Curved surface area =   220 cm²

${\huge{\rm{\underline{\underline{To \: Find :-}}}}}$

⇒ Its radius and height

${\huge{\rm{\underline{\underline{Solution :-}}}}}$

⇒ Let the radius of the base and height of the cylinder be 5x cm and 7x cm respectively.

⇒ As we know that ,

$\sf Curved \; Surface \: of \: a\:cylinder = 2\pi r h = 220\:cm^{2}$

$= 2 \times \frac{22}{7} \times 5x \times 7x = 220\\\\= 2 \times 22 \times 5x \times x = 220\\\\= 220x^{2} = 220\\\\= x^{2} = \frac{220}{220} \\\\= x^{2} = 1 \\\\= x = \sqrt{1} \\\\= x = 1$

⇒ Now ,

Radius = 5x = 5 × 1 = 5 cm

Height = 7x = 7 × 1 = 7 cm

Answer 2

$\sf{Answer}$

Step by step explanation:-

Given :-

In a cylinder,

Ratio of Radius : height = 5:7

CSA = 220cm²

To find :-

Radius & Height of cylinder

Consideration :-

First we will consider

Let the

• Ratio of cylinder = 5x
• Height of cylinder = 7x

Formula implemented:

CSA of cylinder = 2πrh

Solution :-

So,

CSA = 220cm²

2πrh = 220cm²

plugging values!

π = $\sf\dfrac{22}{7}$

2 × $\sf\dfrac{22}{7}$ × 5x × 7x = 220cm²

$\sf\dfrac{ 2×22×5x×7x}{7}$ = 220cm²

$\sf\dfrac{ 44×35x²}{7}$ = 220cm²

$\sf{44 × 5x² }$ = 220cm²

$\sf{220x²}$ = 220cm²

x² = 1cm²

x = 1cm

Finding values :-

5x = 5(1) = 5cm = radius

7x = 7(1) = 7cm = height

So,

Radius of cylinder = 5cm

Height of cylinder = 7cm