Question

genius can only ans this question and the ans of 18question should come 5:3 and 19 question was 7 cm plz help me if you are a indian please see it by zoom

Answer 1

Hey mate !

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$\large{\pink{\boxed{\boxed{\bold{Question \: 18}}}}}$

Given :

The ratio of the radii of two circles is 5:3.

To find :

what is the ratio of their circumference ?

$\underline{\bold{Solution:}}$

Let the radius of the first circle be, r = 5x.

And, the radius of 2ⁿ circle be, R = 3x.

.·. We know that ;

Circumference of circle = 2 π r.

So,

circumference of first circle ;

$\mathsf{ \implies 2 \times \pi \times 5x} \\ \\ \mathsf{ \implies 10x \times \pi}$


Circumference of 2nd circle ;


$\mathsf{ \implies 2 \times \pi \times 3x} \\ \\ \mathsf{ \implies 6x \times \pi}$

Now, their ratios ;

$\large{\mathsf{ \implies \frac{ \cancel{10x} \: {}^{5} \times \cancel {\pi}}{ \cancel{6x} \: {}^{3} \times \cancel{\pi} }}} \\ \\ \mathsf{ \implies \frac{5}{3} } \\ \\ \mathsf{ \implies 5 :3 }$

Hence,

Ratio of their circumference is 5 : 3.

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$\large{\pink{\boxed{\boxed{\bold{Question \: 19}}}}}$

Given :

The circumference of a circle exceeds its diameter by 30 cm.

To find :

Find the radius of the circle. 

$\underline{\bold{Solution:}}$

We know that

Circumference of circle = 2 π r

It is given that, it's diameter exceeds by 30 cm.

So,

2 π r = d + 30

Also, d = 2r

Now,

2πr = 2r + 30

2r ( π - 1 ) = 30

$\mathsf{2r( \frac{22}{7} - 1) = 30} \\ \\ \mathsf{2r( \frac{22 - 7}{7} ) = 30} \\ \\ \mathsf{2r \times \frac{15}{7} = 30} \\ \\ \mathsf{ \frac{30r}{7} = 30} \\ \\ \mathsf{ 30r = 210 } \\ \\ \mathsf{ r = \frac{21 \cancel0}{3 \cancel0} } \\ \\ \mathsf{r = 7 \: cm. }$

Hence,

Radius of circle is 7cm.

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Thanks for the question !

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