Diameter of 2 discs are in the ratio 3:5. What will be the ratio of their areas?
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Diameter of 2 discs are in the ratio 3:5. What will be the ratio of their areas?
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Answer:
Question :
★Diameter of 2 discs are in the ratio 3:5. What will be the ratio of their areas?
Answer :
Given -
D of disc A : D of disc B = 3:5
Let the ratios be 3x and 5x..
So,
Radius of disc A = 3x/2
Radius of disc B = 5x/2
To find -
The ratio of areas of the two discs
= \frac{area \: of \: disc \: a}{area \: of \: disc \: b}=
areaofdiscb
areaofdisca
Area of a circle
= \pi {r}^{2}=πr
2
Ratio of areas =
\frac{\pi {( \frac{3x}{2} )}^{2} }{\pi {( \frac{5x}{2} )}^{2} }
π(
2
5x
)
2
π(
2
3x
)
2
Cancel the π from neumerator and denominator
= \frac{ \frac{9 {x}^{2} }{4} }{ \frac{25 {x}^{2} }{4} }=
4
25x
2
4
9x
2
Simplify, by cancelling x square and 4
=
= \frac{9}{25}=
25
9
So,
the ratio of areas of the two rings would be
9:25