Question

The curved surface area of cylinder is 308 cm sq . . If the ratio of height and radius is 2:5 , then find the height and radius of cylinder .​

Answer 1

$\sf{Answer}$

Step by step explanation:-

Given :-

• Curved Surface area oy cylinder = 308cm²
• Ratio of height, radius = 2:5

To find :-

• Height and Radius of a cylinder

Formula to know :-

• CSA of cylinder is 2πrh

Where

• π = 22/7
• H = height of cylinder
• R = Radius of cylinder

Solution:-

Hence they given ratio of height and radius is 2:5

Let be x

So,

Height of cylinder = 2x

Radius of cylinder = 5x

Substituting in formula

CSA of cylinder = 2πrh

308cm² = 2 × $\sf\dfrac{22}{7}$ × 2x × 5x

308cm² = $\sf\dfrac{2\times22\times5x\times2x}{7}$

308cm² = $\sf\dfrac{440x^2}{7}$

308cm² × 7 = 440x²

2156cm² = 440x²

x² = 2156cm²/440

x² = 4.9cm²

x = $\sf\sqrt{4.9cm^2}$

x = 2.21cm

We have to find radius , height

Radius = 5x = 5(2.21)

Radius =11.05cm

Height = 2x = 2 (2.21)

Height = 4.42

So, height of cylinder is 4.42 and radius of cylinder is 11.05

Answer 2

$\huge \bigstar$$\huge\bold{\mathtt{\purple{A{\pink{N{\green{S{\blue{W{\red{E{\orange{R}}}}}}}}}}}}}$$\huge \Rightarrow$

$\bold {Given:}$

Curved surface area of cylinder $\Rightarrow$ 308².

Ratio of height and radius $\large \Rightarrow$ 2:5

$\bold {Remember\:the \:short \:forms \:of}\Rightarrow$

Curved surface area = CSA

height = h

radius = r

$\large \bold \red{To\:find}\Rightarrow$

height and radius of the cylinder.

$\Large \bold \red{Solution}\Rightarrow$

Let the given ratio 2:5 be $2x$ and $3x$ respectively.

CSA = 2πrh

308cm² = $2\large \frac{22}{7} 2x × 5x$

308cm² = $\large \frac{440x²}{7}$

308cm² × 7 = 440$x²$

2156cm² = 440$x²$

$x²=\large \frac{2156cm²}{440x²}$

$x²=$4.9cm².

$x²= √4.9cm²$

$x = 2.21cm$

height = 2$x$

= 2 × 2.21

= 4.42 cm

radius = 5 $x$

= 5 × 2.21

= 11.05 cm.

.

The height of the cylinder is 4.42 cm and radius is 11.05 cm.