Question

The ratio of the radii of two circles is 4 :5. Find the ratio of their areas

Answer 1

let the radii of the two circles be 4x and 5x

Answer 2

Given:

• The ratio of radii of two circles = 4:5

To find:

• The ratio of their areas.

Solution:

• Let the ratio of radii be 4x and 5x respectively.
• Let their areas be kept as  $a_1$ and $a_2$ .
• We know that area of circle = π$r^2$
• $a_1$ = π*$(4x)^2$ = 16π$x^2$ → (1)
• $a_2$ = π*$(5x)^2$ = 25π$x^2$ → (2)
• Divide equation (1) by equation (2)
• We get, $\frac{a_1}{a_2} = \frac{16}{25}$  
• The ratio of the area of two circles is, $a_1$:$a_2$ = 16:25

∴ The ratio of the areas of the two circles = 16:25.