Question

Find the area of the circle, length of whose circumference is equal to the sum of the lengths of the circumference with radii 15 cm and 13 cm.

Answer 1

Hey there!

》Given: Length of circumference of circle is equal to the sum of the lengths of the circumference with radii 15 cm and 13 cm respectively.

$r_{1}$= 15 cm

$r_{2}$ = 13 cm

Circumference of circle = 2πr

According to your Question:

2πR = $2 \pi r_{1} + 2 \pi r_{2}$

=> 2πR = 2π × 15 + 2π × 13
= 30π + 26π = 56 π

=> R = 28 cm

Thus,
Area of circle = π×(28)²

= 784 × 22 / 7 = 17248 / 7

= 2464 cm²

Hence,
Area of the circle is 2464 cm² .

Cheers!

Answer 2

Circumference of circle C = circumference of circle with radius 15 + circumference of circle with radius 13

Circumference of circle C = 2π15 + 2π13
= 2π(15+13)
= 2 * 22/7 * (28)
= 176 cm.

Now, 2πR = 176 (take radius = R)
= 2*22/7*R = 176
= R = 176*(1/2)*(7/22)
= R = 28 cm

Now, area circle with radius 28 cm
= π * 28² (area of circle = πr²)
(22/7) * 28 * 28
= 2464 cm²

so, the required answer is area of circle = 2464 cm²

Hope it will help you !!!