The circumference of two circle are in the ratio 3:4.and the sum of their area is equal to the area of circle of radius 30cm.find the area of the two circles.
Answers
Here ratio of circumference of two circles is give as 3 : 4
Let radius of one circle be R1 and another circle is R2
[Ratio of circumference is 3:4 and Circumference = 2 × π × Radius ]
∴ ( 2πR1 ) / ( 2πR2 ) = 3 / 4
R1 / R2 = 3 / 4
or R1 : R2 = 3 : 4
Let R1 = 3r and R2 = 4r (Ratio is 3:4)
According to question
Area of circle with R1 + Area of Circle with R2 = Area of circle with Radius 30
∴ π (3r)² + π (4r)² = π (30)² [Area of circle = π (radius)² ]
Dividing whole equation by π
(3r)² + (4r)² = (30)²
9r² + 16r² = 900
25r² =900
r² = 36
r = 6
∴ R1 = 3r = 18 cm
R2 = 4r = 24 cm
Area of circle with radius R1( 18 cm) = π (18)² = 324π cm² or 7628/7 cm²
Area of circle with radius R2 (24 cm) = π (24)² = 576π cm² or 12672/7 cm²
Step-by-step explanation:
lcircumference =3 area
2πr = 3π r^2
2r = 3r^2
2= 3r
3/2= r