Question

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm3 . find its radius and ratio of curved.to its surface area

Answer 1

given r:h = 5:7
let r=5x and h=7x
volume=πr²h
550 = 22×5x×5x×7x/7
550 = 550x³
x³ = 1
x = 1
radius = 5×1 = 5cm , height = 7cm
curved surface area = 2πrh = 2×22×5×7/7 = 220cm²
total surface area = 2πr(r+h) = 2×22×5(5+7)/7 = 377.14cm²
ratio= 7:12

Answer 2

let,
radius = r = 5x
height=  h = 7x
volume = v = 550cm³
V = πr²h
550 = 22/7 × (5x)² × 7x
550 = 22 × 25 x³
       = 550 x3
x³ = 1
x= 1
therefore, length = 5x = 5×1= 5 cm
                 height = 7x = 7×1 = 7 cm
c.s.a of cylinder = 2 π r h
                          = 2 × 22/7 × 5 × 7
                          = 220 cm²
t.s.a of cylinder = 2πr(r+h)
                         = 2 ×22/7× 5(5 +7)
                         = 377.14 cm²
ratio of c.s.a to t.s.a = 220 :377.14
                                 = 7 :12