Question

the radius and the height of a cylinder are in the ratio 5:7 and its volume is 550 cm ³ find its radius .​

Answer 1

Answer:

• Radius of a cylinder = 5 cm
• Height of a cylinder = 7 cm

Step-by-step explanation:

Given that:

• The radius and the height of a cylinder are in the ratio 5 : 7.
• Its volume is 550 cm³.

Let us assume:

• Radius of a cylinder = 5x
• Height of a cylinder = 7x

Formula used:

• Volume of a cylinder = πr²h

Here,

• Radius is denoted as r.
• Height is denoted as h.

Finding the radius and height:

Volume of a cylinder = πr²h

• Putting the values.

→ 550 = π × (5x)² × 7x

• 7 cancelled ∵ π = 22/7

→ 550 = 22 × 25x² × x

→ 550 = 550x³

• 550 cancelled both sides.

→ x³ = 1

→ x = 1

Now,

• Radius = 5x = 5 × 1 = 5 cm
• Height = 7x = 7 × 1 = 7 cm

Answer 2

${\bf{Given\::}}$

• The radius and the height of a cylinder are in the ratio 5 : 7.

• Volume of the cylinder is 550 cm³.

$\\ {\bf{To\: Find\::}}$

• Radius of the cylinder.

$\\ {\bf{Solution\::}}$

Let,

• Radius of the cylinder is 5x.

• Height of the cylinder is 7x.

As we know that,

☛ Volume of a cylinder is given as,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Volume\:=\:\pi\:r^2\:h\:}\:{\Large\mid}\:\green\bigstar$

➠ 550 = $\tt{\dfrac{22}{7}}$ × (5x)² × 7x

➠ 550 = 22 × 25x² × x

➠ 25x³ = $\tt{\dfrac{550}{22}}$

➠ 25x³ = 25

➠ x³ = $\tt{\dfrac{25}{25}}$

➠ x = $\tt{\sqrt[3]{1}}$

➠ x = 1

Hence,

➛ Radius = 5x = 5 × 1 = 5 cm

∴ Radius of the cylinder is 5 cm.