Question

The ratio of areas of circle A to circle B is 5:4. If the radius of circle B is 28cm, what is the area of circle A?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The radius of circle A is 31.3 cm

Step-by-step explanation:

Given as :

The ratio of areas of circle A to circle B is 5 : 4

The radius of Circle B = R = 28 cm

Let The radius of circle A = r cm

According to question

∵ Area of circle = π × radius²

So, Area of circle A = π × (r cm)²

And

Area of circle B = π × R²

So, Area of circle B = π × (28 cm)²

∵ ratio of areas of circle A to circle B is 5 : 4

i,e  $\dfrac{Area of circle A}{Area of circle B}$  =  $\dfrac{5}{4}$

Or,  $\dfrac{\Pi r^{2}}{\Pi 28^{2}}$  = $\dfrac{5}{4}$

Or,  $\dfrac{r^{2} }{28^{2} }$ = $\dfrac{5}{4}$

Or,  r² = $\dfrac{5}{4}$  × 28²

Or, r² = $\dfrac{5}{4}$  × 784

Or,  r² =  980

∴   r = √980

i.e  r = 31.3 cm

So, The radius of circle A = r = 31.3 cm

Hence, The radius of circle A is 31.3 cm  Answer