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.
Answers
Step-by-step explanation:
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
Radius = 4.99 cm
Height = 7.03 cm
Volume = 550.14 cm³
