Math, asked by namratalokare2, 1 year ago

the radius and height of a cylinder are in the ratio 4:7.find the radius and height of the cylinder if it's volume is 1188cu cm. also find the total surface area.

Answers

Answered by TPS
88
radius and height are in the ratio 4:7
let radius, r = 4x
height, h = 7x

volume = πr²h
⇒ 1188 = π × (4x)² × 7x
⇒ 1188 = (22/7) ×16x² × 7x
⇒ 1188 = 22×16x² × x
⇒ 1188 = 352x³
⇒ x³ = 1188/352 = 27/8
⇒ x = ∛(27/8) = 3/2 = 1.5cm

radius = 4x = 4×1.5 = 6cm
height = 7x = 7×1.5 = 10.5 cm

TSA = 2πr(r+h)
        = 2×(22/7)×6(6+10.5)
        = 836.28 cm²

namratalokare2: ok i got the answer
TPS: :)
Answered by Revolution
20
radius and height are in the ratio 4:7
 radius( r) = 4k
height( h )= 7k
volume(v)=[tex] \pi r^{2} h \\ = \frac{22}{7} *(4k) ^{2} *7k \\ \\ \frac{22}{7}*112k ^{3} \\ \\ volume=352 k^{3} \\ volume=1188 cm ^{3} \\ \\ 352 k^{3} =1188 \\ k ^{3} =1188/352=3.375 \\ k=1.5 \\
radus=4k=4*1.5=6 [/tex]
height = 7x = 7×1.5 = 10.5 cm

TSA = 2πrh+2πr²
        = 2*22/7*6*10.5+2*22/7*36
        = 836.28 cm²

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