Question

Q11. Ratio between height of 2 cylinder is in the
ratio 3:5. Their volumes are in the ratio 27:80. Find
ratio between their radius.
(a)1/2 (b)2/3 (c)3/4 (d)4/5 (e)None of these​

Answer 1

Step-by-step explanation:

your answer is c.3:4

.........

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Ratio between height of 2 cylinder is 3:5

• Ratio between volume of the two cylinder is 27:80

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Ratio between their radius

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that , Ratio between height of 2 cylinder is 3:5

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So,

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• Height of 1st cylinder 3H

• Height of 2nd cylinder 5H

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• Let the radius of 1st cylinder be R

• Let the radius of 2nd cylinder be R'

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$\underline{\bold{\texttt{Volume of cylinder :}}}$

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➠ πr²h ⚊⚊⚊⚊ ⓵

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Where ,

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• r = Radius

• h = Height

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$\underline{\bold{\texttt{Volume of 1st cylinder :}}}$

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• r = R

• h = 3H

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⟮ Putting the above values in ⓵ ⟯

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➜ πr²h

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➠ π(R)²3H ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Volume of 2nd cylinder :}}}$

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• r = R'

• h = 5H

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⟮ Putting the above values in ⓵ ⟯

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➜ πr²h

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➠ π(R')²5H ⚊⚊⚊⚊ ⓷

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Also given that ,Ratio between volume of the two cylinder is 27:80

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From ⓶ & ⓷

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➜ $\sf \dfrac { \pi(R) ^2 3H } { \pi(R') ^2 5H } = \dfrac { 27 } { 80 }$

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➜ $\sf \dfrac { (R) ^2 3} { (R') ^2 5} = \dfrac { 27 } { 80 }$

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➜ $\sf \dfrac { (R) ^2 } { (R') ^2 } = \dfrac { 27 \times 5} { 80 \times 3}$

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➜ $\sf \dfrac { (R) ^2 } { (R') ^2 } = \dfrac { 9} { 16}$

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➜ $\sf \bigg(\dfrac { R} { R' }\bigg)^2 = \dfrac { 9} { 16}$

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➜ $\sf \dfrac { R } { R' } = \sqrt { \dfrac { 9} { 16}}$

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➨ $\sf \dfrac { R} { R' } = \dfrac { 3} { 4}$

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∴ The ratio between their radius is 3:4 or 3/4

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• Hence option c) 3/4 is correct