Question

A solid cylinder has a total surface area of 462 cm². Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

Answer 1

Total surface area of a cylinder = 462 cm²

As per given statement: 

Curved or lateral surface area = \(\frac{1}{3}\) (Total surface area) 

⇒ 2πrh = \(\frac{1}{3}\)(462) 

⇒ 2πrh = 154

⇒ 2 x \(\frac{22}{7}\) x r x h = 154

⇒ h = \(\frac{49}{2r}\) ….(1)

Again, 

Total surface area = 462 cm² 

2πr(h + r) = 462 

2πr(\(\frac{49}{2r}\) + r) = 462 

or 49 + 2r² = 147 

or 2r² = 98 

or r = 7 

Substitute the value of r in equation (1),

h = \(\frac{49}{2}\)(7) 

= \(\frac{49}{14}\)

= \(\frac{7}{2}\)

Height (h) =  \(\frac{7}{2}\) cm

Radius = 7 cm and height =  \(\frac{7}{2}\) cm of the cylinder