Question

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Answer 1

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

$= \frac{area \: of \: disc \: a}{area \: of \: disc \: b}$

Area of a circle

$= \pi {r}^{2}$

Ratio of areas =

$\frac{\pi {( \frac{3x}{2} )}^{2} }{\pi {( \frac{5x}{2} )}^{2} }$

Cancel the π from neumerator and denominator

$= \frac{ \frac{9 {x}^{2} }{4} }{ \frac{25 {x}^{2} }{4} }$

Simplify, by cancelling x square and 4

=

$= \frac{9}{25}$

So,

the ratio of areas of the two rings would be

9:25

★Points to know

• Try to represent ratios in simplest forms

• Try to write formula to avoid confusion

•One major flaw can be that students forget to convert Diameter into Radius.