What length of solid cylinder $2 c m$ in diameter must be taken to recast into a hollow cylinder of external diameter $20 c m$ , $0.25 c m$ thick and $15 c m$ long?

74.06

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88

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78

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66.38

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Solution

The correct option is A $74.06$ cm
Diameter $= 2 c m$
Radius $= 1 c m$
Height $= h$
Hollow cylinder of external diameter $20 c m$
Radius $= 10 c m$
Thickness $= 0.25 c m$
So, Internal radius $=$ External radius $-$ Thickness
$r_{1} = 10 - 0.25 = 9.75 c m$

Length $= 15 c m$
As per question,
Volume of solid cylinder $=$ Volume of hollow cylinder

$π r^{2} h = π h (R^{2} - {r_{1}}^{2})$

$1^{2} h = 15 (10^{2} - {9.75}^{2})$

$h = 74.06 c m$

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What length of solid cylinder 2cm in diameter must be taken to recast into a hollow cylinder of external diameter 20cm, 0.25cm thick and 15cm long?

What length of solid cylinder $2 c m$ in diameter must be taken to recast into a hollow cylinder of external diameter $20 c m$ , $0.25 c m$ thick and $15 c m$ long?