Question

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

Answer 1

Let the radius and height of the cylinder be r and h, respectively.

Curved surface area of cylinder = 2πrh

Area of base = πr²

Sum of areas of bases = 2πr² 

According to the question,

4 × Curved surface area = 6 × Sum of areas of bases

4 × 2πrh = 6 × 2πr²

⇒ 8πrh = 12πr²

⇒ 2h = 3r

⇒ `r = 2/3 h`  

∴ `r = 2/3 xx 12 = 8 cm`   ...[∵ h = 12 cm, given]

∴ Curved surface area of the cylinder = 2πrh

= `2 xx 22/7 xx 8 xx 12`

= `(44 xx 8 xx 12)/7`

= 603.428 cm²