Question

The total surface area of a cylinder is 6512 cm² and the circumference of its bases is 88 cm. Find:
(i) its radius
(ii) its volume

Answer 1

Let r be the radius and h be the height of the given cylinder.
Circumference = 2πr = 88 cm (Given)

⇒ `2 xx 22/7 xx r = 88`cm

⇒ `r = 88 xx 7/22 xx 1/2`

⇒ r = 14 cm

Total surface area = `2pir(h + r) = 6512` cm² (Given)

⇒ `88(h + 14) = 6512` (∵ `2pir = 88` cm and r = 14 cm)

⇒ `h + 14 = 6512/88`

⇒ h + 14 = 74 ⇒ h = 60 cm

∴ Volume of the cylinder = `pir^2h`

= `22/7 xx (14)^2 xx 60` cm³ = 36960 cm³