Question

the vertical height of a right circular cylinder is three times its diameter and its volume is 54pi cm^3.find height
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Answer 1

Given :

• vertical height of a right circular cylinder is three times its diameter

• volume = 54π cm³

To find :

• height of the right circular cylinder

Formula used :

• Volume of cylinder = π r² h

• Radius = ( diameter/2)

Solution :

Let diameter be x.

Radius = x/2

Height = 3x

volume = 54π cm³

Volume of cylinder = π r² h

54π = π r² h

54π = π ( x/2)² (3x)

54 π / π = ( x/2)² (3x)

54 = (x²/ 4) (3x)

( 54×4) / 3 = x³

18×4 = x³

72 = x³

(72)^1/3 = x

Therefore height = 3× (72)^1/3

Answer :-

$h = 3 \sqrt[3]{72} \: cm$

where h = height

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Learn more :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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