Question

the volume of a cylinder is 308 centimetres cube it is the height is 8 cm find its the lateral surface area and total surface area

Answer 1

Given that,
Curved surface area : Total surface area = 1:2
Curved surface area : 616 = 1:2

Curved surface area = 616 / 2 = 308
2πrh / 2πr(h+r) = 1/2
h / (h+r) = 1/2
h+r = 2h
⇒ h = r

Curved surface area = 2πrh = 2πr2 = 308 [Since h = r]

2 x 22/7 x r2 = 308
r2 = 308 x 7/44
r2 = 49
r = 7 cm

⇒ h = 7 cm

Volume of the cylinder = πr2h 
= 22/7 x 7 x 7 x 7
= 1078 cm3

Volume of the cylinder is 1078 cu cm.