Question

The radii of two circles are 19cm and 9 cm respectively. Find the radius and area of the circle which has circumferences is equal to sum of circumference of two circles.

Answer 1

Radius of 1^st circle = 19cm

Radius of 2^nd circle = 9 cm

Circumference of 1^st circle = 2(19) = 38𝜋 cm

Circumference of 2^nd circle = 2𝜋 (9) = 18𝜋 cm

Let radius of required circle = R cm

Circumference of required circle = 2𝜋R = 𝑐₁ + 𝑐₂

2𝜋R = 38𝜋 + 18𝜋

2𝜋R = 56𝜋

R = 28 cms

Area of required circle = 𝜋r²

=`22/7× 28 × 28`

= 2464 𝑐𝑚²