Question

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm³ . What will be its radius​

Answer 1

GIVEN :-

• Ratio and height of a cylinder are in ratio 5:7.
• Volume of the cylinder is 550cm³.

TO FIND :-

• Radius of the cylinder.

TO KNOW :-

★ Volume of Cylinder = πr²h

• 'r' is radius and 'h' is height of the Cylinder.

SOLUTION :-

As radius and height are in ratio , let the common multiple be 'x'.

Radius of the Cylinder be 5x and height of the cylinder be 7x as they are in ratio of 5:7.

We know,

Volume of Cylinder = πr²h -----(1)

We have ,

• Volume of Cylinder = 550cm³
• Radius (r) = 5x
• Height (h) = 7x

Putting values in equation (1) ,

→ 550 = π × (5x)² × (7x)

→ 550 = (22/7) × (25x²) × (7x)

→ 550 = (22/7) × 175x³

→ 550 = 3850x³/7

→ 550 × 7 = 3850x³

→ 3850 = 3850x³

→ x³ = 1

→ x = ³√1

→ x = 1

Hence ,

• Radius = 5x = 5(1) = 5cm

Hence , radius of the Cylinder is 5cm.

MORE TO KNOW :-

★ Volume of Cube = edge³

★ Volume of Cuboid = l × b × h

★ Volume of Cone = (1/3)πr²h

★ Volume of Sphere = (4/3)πr³

★ Volume of Hemisphere = (2/3)πr³

Answer 2

$\;\;\bf{\;\;\blue{Given : }}$

Ratios -

• Radius and height of cylinder = 5:7
• Volume = 550 cm³

$\;\;\bf{\;\;\red{To \: find : }}$

• Radius of the cylinder

$\;\;\bf{\;\;\green{Solution :}}$

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

We know , that

Volume = 550 cm³

$\;\;\bf{\rightarrow\;\;\blue{ \frac{22}{7} \times (5x {}^{2}) \times 7x = 550 }}$

$\;\;\bf{\rightarrow\;\;\blue{22 \times 25x³ = 550}}$

$\;\;\bf{\rightarrow\;\;\red{x = 1 \: cm}}$

$\sf Hence , \\ \sf \: The \: radius \: of \: cylinder = 5x = 5cm$