Question

the radius and height of a cylinder are in ratio 5 is to 7 and it's volume 550cm cube find its radius​

Answer 1

$\large\underline\pink{Given:-}$

• The radius and height of a cylinder are in ratio 5 is to 7.
• It's volume 550cm cube

$\large\underline\pink{To find:-}$

• Fine the radius of the cylinder ....?

$\large\underline\pink{Solutions:-}$

• Let the radius of a cylinder be 5x.
• Let the height of a cylinder be 7x.

Volume of cylinder = πr²h

$\: \: \: \: \: \leadsto \: \: \frac{22}{7} \: \times \: {(5x)}^{2} \: \times \: {7x} \: \: = \: \: {550}$

$\: \: \: \: \: \leadsto \: \: \frac{22}{7} \: \times \: {25x}^{2} \: \times \: {7x} \: \: = \: \: {550}$

$\: \: \: \: \: \leadsto \: \: {22} \: \times \: {25x}^{2} \: \times \: {x} \: \: = \: \: {550}$

$\: \: \: \: \: \leadsto \: \: {550x}^{2} \: \times \: {x} \: \: = \: \: {550}$

$\: \: \: \: \: \leadsto \: \: {550x}^{3} \: \: = \: \: {550}$

$\: \: \: \: \: \leadsto \: \: {x}^{3} \: \: = \: \: \frac{550}{550}$

$\: \: \: \: \: \leadsto \: \: {x}^{3} \: \: = \: \: {1}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {(1)}^{\frac{1}{3}}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {1}$

• Now, The radius of the cylinder is 5x.

⟹ 5 × 1

⟹ 5 cm.

• The height of the cylinder is 7x.

⟹ 7 × 1

⟹ 7 cm.

• Hence, The radius of the cylinder is 5 cm.

$\large\underline\pink{More \: Information:-}$

• Volume of cylinder ( Area of base × height ).

= (πr²) × h

= πr²h

• Curved surface = ( Perimeter of base ) × height.

= (2πr) × h

= 2πrh

• Total surface are = Area of circular ends + curved surface area.

= 2πr² + 2πrh

= 2πr(r + h)

• Where, r = radius of the circular base of the cylinder.

h = height of cylinder.

Answer 2

$\star$ $\large\underline\mathrm\red{Given :}$

• The radius of a cylinder in ration is 5:7.

• Height of a cylinder is 550cm cube.

$\large\underline\mathrm\red{To \: find :}$

The radius of a cylinder ?

$\huge\mathbf\red{Solution :-}$

→ Let the radius of a cylinder be 5x.

→ Let the radius of a cylinder be 7x.

• Volume of a cylinder = πr²h

$\frac {22}{7} \times (5x)² \times 7x = 550$

$\frac {22}{7} \times (25x)² \times 7x = 550$

$22 × 25x² × x = 550$

$550x² × x =550$

$550x³ = 550$

$x³ = \frac {550}{550}$

$x³ = 1$

$x = (1)⅓$

Here, we know that radius of a cylinder is 5x.

$= 5 × x$

$= 5 × 1$

$→ 5cm$

•°• Radius of a cylinder is 5cm.

Now, height of a cylinder is 7x.

$= 7 × x$

$= 7 × 1$

$→ 7cm$

•°• Height of a cylinder is 7cm.

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$\large\underline\mathrm\red{Formulas \: used :}$

• Volume if a cylinder = ( area of base × area of height)

= πr²h

Here, r = radius and h = height.

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