Question

The radius and height of a cylinder are in the ratio of 5 : 7 and its volume is 550 cm. Find its radius. (Take π = 22/7)

Answer 1

Let the radius of the base and height of the cylinder be 5x cm and 7x cm respectively.
Then,
Volume = 550 cm³
⇒ ${\displaystyle \frac{22}{7}\times {\left(5x\right)}^2\times 7x=550}$....( Use, r = 5x, h = 7x and volume = πr²h )

⇒ ${\displaystyle \frac{22}{7}\times 25x^2\times 7x=550}$

⇒ 22 x 25x³ = 550
⇒  550x³ = 550
⇒  x³ = 1
⇒  x = 1
Hence, radius of the cyclinder = 5x cm = ( 5 x 1 ) cm = 5 cm.