Question

The curved surface area of a cylinder is 264 m² and its volume is 924 m³, then what is the ratio between its diameter and height?
1. 7 : 6
2. 6 : 7
3. 3 : 7
4. 7 : 3

Answer 1

Correct Answer - Option 4 : 7 : 3

Given:
Curved surface area of a cylinder = 264 m2 
Volume of a cylinder = 924 m3

Concept used:
Curved surface area of a cylinder = 2 × π × r × h
Volume of a cylinder = π × r² × h

Calculation: 
Let radius and height of a cylinder be r and h respectively.
Curved surface area of a cylinder = 264
⇒ 2 × 22/7 × r × h = 264
⇒ r × h = (264 × 7)/44
⇒ r × h = 6 × 7
⇒ r × h = 42      ----(1)
Volume of a cylinder = 924 m3
⇒ 22/7 × r² × h = 924
⇒ r² × h = (924 × 7)/22
⇒ r × r × h = 42 × 7
From equation (1),
⇒ r × 42 = 42 × 7
⇒ r = (42 × 7)/42
⇒ r = 7
Diameter = 2 × r = 14
Put the value of r in equation (1),
⇒ 7 × h = 42
⇒ h = 6
Ratio between the diameter and the height = 14 : 6 = 7 : 3
∴ The ratio between its diameter and height is 7 : 3.