Question

the ratio of height of right cylinder to its radius is 1:2and its curved surface area is 616m^2.Find its diameter.​

Answer 1

Answer:

• Diameter of right cylinder is 28 cm.

Step-by-step explanation:

Given :-

• Ratio of height and radius of right cylinder is 1:2.
• Curved surface area of cylinder is 616 m².

To find :-

• Diameter of cylinder.

Solution :-

Let, height of cylinder be 1x or x.

And, Radius of cylinder be 2x.

So,

Curved surface area of cylinder = 2πrh

Where,

• r is radius of cylinder.
• h is height of cylinder.

Put values :

$\longrightarrow$ 616 = 2πrh

$\longrightarrow$ 616 = 2 × 22/7 × 2x × x

$\longrightarrow$ 616 = 44/7 × 2x²

$\longrightarrow$ 616 × 7 = 44 × 2x²

$\longrightarrow$ 4312 = 44 × 2x²

$\longrightarrow$ 4312/44 = 2x²

$\longrightarrow$ 98 = 2x²

$\longrightarrow$ 98/2 = x²

$\longrightarrow$ 49 = x²

$\longrightarrow$ √49 = x

$\longrightarrow$ x = 7

Measures :-

Height = x = 7 cm.

Radius = 2x = 2 × 7 = 14 cm.

We know,

Diameter = Radius × 2

$\longrightarrow$ Diameter = 14 × 2

$\longrightarrow$ Diameter = 28

Therefore,

Diameter of right cylinder is 28 m.

Answer 2

To Find:-

• Find it's diameter.

Given:-

• The ratio of height of cylinder to is radius is 1 : 2.
• It's curved surface area is 616m².

Solution:-

１. Let the height of the cyclinder be "x"

２. And radius be " 2x '

Curved surface area of cyclinder = 2πrh

Substituting Values:-

$\tt\implies \: 616 = 2 \times \dfrac{22}{7} \times 2x \times x$

$\tt\implies \: 616 = \dfrac{44}{7} \times {2x}^{2}$

$\tt\implies \: \dfrac{616 \times 7}{44} = {2x}^{2}$

$\tt\implies \: {x}^{2} = \dfrac{98}{2}$

$\tt\implies \: x = \sqrt{49}$

$\tt\implies \: x = 7$

Hence,

• Height = 7 cm
• Radius is 2x = 2(7) = 14 cm
• Diameter = Radius × 2 = 28 cm