Question

Ratio between heights of two cylinder in the ratio 3:5. Their volumes are in the ratio 27:80. Find ratio between their radius ?
A) 1:3
B) 2:1
C) 3:4
D) 4:7

Answer 1

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Here is your answer in the attachment.

The answer is Option C) 3:4.

Explaination:

In the attachment.

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Answer 2

Hello Friend

Here is your answer

As we know the formula

Volume of the cylinder is πr^2h

so Volume of I cylinder is
$v_{1} = \pi \times {r}^{2} \times h \\ 27 = \pi \times {r _{1} }^{2} \times 3 \\ r {}^{2} _{1} = \frac{27}{3 \times \pi} \\ {r _{1} }^{2} = \frac{9}{\pi}$
Hence

Volume of II CYLINDER IS
$v _{2} = \pi \times {r _{2} }^{2} \times 5 \\ {r _{2}}^{2} = \frac{80}{\pi \times 5} \\ {r _{2} }^{2} = \frac{16}{\pi}$

Ratio of their Radius is
$\frac{ {r _{1} }^{2} }{ {r _{2} }^{2} } = \frac{ \frac{9}{\pi} }{ \frac{16}{\pi} } \\ \\ ( \frac{ {r _{1} }^{2} }{ {r _{2}}^{2} } ) = \frac{9}{16} \\ \\ \frac{r _{1} }{r _{2} } = \sqrt{ \frac{9}{16} } = \frac{3}{4}$
Therefore Option (C) 3: 4 is your answer

Hope it helps you