Question

The sum of the height and the radius of a cylinder is 28 cm and its total surface area is 616 cm², find the volume of the cylinder.

Answer 1

Let height = h
radius = r
h+ r = 28cm  ...(given)
∴ h = 28 - r cm
Total surface area of cylinder
= 2πrh + 2πr²
2πr(28 - r) + 2πr² = 616
56πr - 2πr² + 2πr² = 616
56πr = 616

r = `(616)/(56pi)`
r = 3.5cm
h = 28 - r
= 28 - 3.5
= 24.5cm
Volume of cylinder
= πr²h
= π(3.5)² x 24.5
= 943cm³
∴ Volume of cylinder is 943cm³.