Question

The radii of two cricles are in the ratio 3:8 If the difference between their areas 2695 pie cm square ,find the area of the smaller cricle​

Answer 1

QUESTION:

The radii of the two circles are in the ratio 3:8. If the difference between their area is 2695 pi sq.cm, find the area of the smaller circle.

ANSWER:

The area of the smaller circle is 1386 sq.cm

STEP BY STEP EXPLANATION:

Radius of the 1st circle = 3x  ( smaller radius )

Radius of the 2nd circle = 8x  ( Larger radius )

Area of the circle = $\pi r^{2}$ sq.units

Difference between their areas = Area of big circle - Area of small circle

2695$\pi$ = $\pi [(8x)^{2} -(3x)^{2} ]$

2695$\pi$ = $\pi [(64x^{2} -9x^{2} )]$

2695 = $55x^{2}$

= 2695/55

$x^{2} = 49$

x = 7

So, radius of larger circle =  56 cm

      radius of smaller circle = 21 cm

Area of smaller  circle = $\pi r^{2}$  sq.units

   

 = $\pi (21^{2} )$

 = $\frac{22}{7} (441)$

 = 63(22)

 = 1386 sq.cm

Answer 2

ANSWER:

The area of the smaller circle is 1386 sq.cm

STEP BY STEP EXPLANATION:

Radius of the 1st circle = 3x ( smaller radius )

Radius of the 2nd circle = 8x ( Larger radius )

Area of the circle = πr² sq.units

Difference between their areas = Area of big circle - Area of small circle

2695π = π(64x²) - π(9x²)

2695π = 55πx²

2695 = 55x²

x² = 2695/55

x² = 49

x = 7

So, radius of larger circle = 56 cm

radius of smaller circle = 21 cm

Area of smaller circle = πr² sq.units

= (22/7)(21)²

= (22/7)(441)

= 63(22)

= 1386 sq.cm