Question

two right circular cylinder of equal volume have their height in the ratio 4 is to 9 find the ratio of their curved surface area​

Answer 1

SOLUTION:-

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Given:

•Two right circular cylinder of equal volume have their height in the ratio 4:9.

To find:

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The ratio of their curved surface area.

Explanation:

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•Let r1,h1 be the radius and height of cylinder 1.

•Let r2,h2, be the radius & height of the cylinder 2.

We know that, formula of the volume of cylinder:

πr²h

According to the question:

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Volume of cylinder 1= volume of cylinder 2.

• πr1²h1 = πr2²h2.

$\frac{\pi \: r1 {}^{2} h1}{\pi \: r2 {}^{2} h2} \\ \\ = > \frac{r1 {}^{2} }{r2 {}^{2} } = \frac{h2}{h1} \\ \\ = > \frac{r1}{r2} = \sqrt{ \frac{9}{4} } \\ \\ = > \frac{r1}{r2} = \frac{3}{2}$

Hence,

r1 : r2= 3:2.

Now,

Formula:Curved Surface Area of cylinder

Formula: 2πrh

Therefore,

In first cylinder:

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$= > 2 \times \frac{22}{7} \times 3 \times 9 \\ \\ = > \frac{44}{7} \times 27 \\ \\ = > \frac{1188}{7} sq.units$

&

In second Cylinder:

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$= > 2 \times \frac{22}{7} \times 2 \times 4 \\ \\ = > \frac{44}{7} \times 8 \\ \\ = > \frac{352}{7} sq.unit$

:)