Question

The radii of two circles are 13 cm and 5cm.What is the radius of the circle which has an area equal to the difference of the areas os the 2 circles/

Answer 1

The radius of the circle which has an area equal to the difference of the areas of the two circles is 12 cm

Step-by-step explanation:

Given as :

The radius of first circle = $r_1$ = 13 cm

The radius of second circle = $r_2$ = 5 cm

Let The radius of other circle = R cm

According to question

∵  Area of circle =  π × radius²

Area of first circle = π × $r_1$ ²

Or, $A_1$  = π × (13 cm)²

Area of second circle = π × $r_2$ ²

Or, $A_2$  = π × (5 cm)²

Again

Area of other circle with radius R = π × R²

now, A/Q

Area other circle with radius R = Area of circle with radius $r_1$ - Area of circle with radius $r_2$

Or,  π × R²  = π × $r_1$ ² - π × $r_2$ ²

removing π from both side

i.e   R²  = $r_1$ ² - $r_2$ ²

Or,  R²  = ( 13 cm )² - ( 5 cm) ²

Or,  R²  = 169 cm² - 25 cm²

Or, R²  = 144 cm²

∴   R = √144

i.e  R = 12 cm

So, The radius of other circle = R = 12 cm

Hence, The radius of the circle which has an area equal to the difference of the areas of the two circles is 12 cm . Answer

Answer 2

Answer:

Given as :

The radius of first circle = r_1r

1

= 13 cm

The radius of second circle = r_2r

2

= 5 cm

Let The radius of other circle = R cm

According to question

∵ Area of circle = π × radius²

Area of first circle = π × r_1r

1

²

Or, A_1A

1

= π × (13 cm)²

Area of second circle = π × r_2r

2

²

Or, A_2A

2

= π × (5 cm)²

Again

Area of other circle with radius R = π × R²

now, A/Q