Question

the radius and height of a cylinder are in the ratio 5:7 the volume is 550 cm² find its diameter

Answer 1

r:h=5:7
V=550cm²
d=?

V=πr²h
550=22/7×5y×5y×7y
550×7÷22=25y²×7y
1=y³
y=1cm

⇒r =5cm
d =2r
  =2×5
  =10cm

Answer 2

let radius be 5x and height be 7x

V of Cylinder = π $r^{2}$ h
550 = 22/7 * 5x * 5x * 7x
550 * 7/22 = 175 $x^{3}$
25 * 7 * 1/175 = $x^{3}$
175/175
1 = $x^{3}$
x = 1

Sub x , radius = 5cm and height = 7cm
Diameter = 2 * radius
Diameter = 2*5 = 10 cm