Question

Diameter of 2 discs are in the ratio 3:5. What will be the ratio of their areas?

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 represent ratios in simplest forms• Try to write formula to avoid confusion

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.

Answer 2

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