# 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

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let r=5x and h=7x

volume=

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

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