Question

The sum of the radius and the height of a cylinder is 12 cm and the total surface area of the cylinder is
377.14 cm. Find the height and the volume of the cylinder.
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Height of cylinder = 7 cm

Volume of cylinder = 550 cm³

Step-by-step explanation:

Given that:

• The sum of the radius and the height of a cylinder is 12 cm.
• The total surface area of cylinder is 377.14 cm.

To Find:

• The height and the volume of the cylinder.

Formula used:

• T.S.A = 2πr(r + h) sq. unit
• V = πr²h cubic unit

Where,

• T.S.A = Total surface area of cylinder
• V = Volume of cylinder
• r = Radius of cylinder
• h = Height of cylinder

Finding the height of cylinder:

→ 377.14 = 2 × 22/7 × r × (12)

→ r = (377.14 × 7)/(2 × 22 × 12)

→ r = 5 (approx.)

Now,

→ r + h = 12 cm [Given]

→ 5 + h = 12 cm

→ h = 12 - 5 = 7 cm

∴ Height of cylinder = 7 cm

Finding the volume of cylinder:

• Volume of cylinder = π × (5)² × 7 cm³
• Volume of cylinder = (22 × 25 × 7)/7 cm³
• Volume of cylinder = 550 cm³