Question

The lateral surface area of a cylinder gets reduced by 75piecm? if its diameter is reduced by
5 cm, while keeping the height same. It increases by 100piecm, it height is increased by 5 cm
while keeping the diameter same. Find the diameter and height of the cylinder.

Answer 1

$\tt\huge{\red{Answer:-}}$

Diameter of cylinder=20/cm=6.36cm

Height of cylinder=15/cm=4.77cm

Step-by-step explanation:

Let the diameter be D.

Let the height be H.

Lateral surface area=DH

As said in question diameter is reduced by 5cm.So,

DH-75=(D-5)H

-5H=-75

H=15/cm

As said in question height is increased by 5 cm.So,

DH+100=D(H+5)

5D=100

D=20

Diameter of cylinder=20/cm=6.36cm

Height of cylinder=15/cm=4.77cm

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Answer 2

⋆ $\bold{\underline{\underline{\rm{\pink{Given:-}}}}}$

• The lateral surface area of a cylinder gets reduced by 75piecm? if its diameter is reduced by 5 cm, while keeping the height same. It increases by 100piecm, it height is increased by 5 cm while keeping the diameter same.

⋆ $\bold{\underline{\underline{\rm{\blue{To \; Find:-}}}}}$

• The diameter and height of the cylinder.

⋆ $\bold{\underline{\underline{\rm{\red{Solution:-}}}}}$

$\ \ \ \bullet$ Let the diameter of cylinder be D.

$\ \ \ \bullet$ Let the height of cylinder be H.

$\ \ \ \bullet$ Then, Lateral Surface Area = πDH

⋆ $\bold{\underline{\underline{\rm{\pink{According\:to\; question:-}}}}}$

✦ Diameter is reduced by 5cm and L.S.A is reduced by 75π cm². So,

$\implies \sf{ \pi DH - 75 = \pi (D - 5)H}$

$\implies \sf{ -5 \pi H = - 75}$

$\implies \sf{H = \dfrac{15}{ \pi}}$

✦ Height is increased by 5cm and L.H.S increased by 100π cm² So,

$\implies \sf{ \pi DH + 100 = \pi D(H + 5)}$

$\implies \sf{5 \pi D = 100}$

$\implies \sf{D = \dfrac{20}{ \pi}}$

Hence,

★ The diameter of the cylinder = $\sf{ \dfrac{20}{ \pi} = 6.36 cm}$

★ And, The Height of the cylinder = $\sf{ \dfrac{15}{ \pi} = 4.77 cm}$

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