Question

The circumference of a circle is equal to the
sum of the circumferences of two circles
having diameters 34 cm and 28 cm. The
radius of the new circle is .
.....​

Answer 1

Answer:  

2πR = 2πr1 + 2πr2

        = 2×22/7 ×17 + 2×22/7 ×14

        = 784/7 + 88 = 1400/7 = 200 cm

2×22/7×R = 200

44/7 ×R = 200

R = 200×7/44 = 1400/7 = 31.8 cm

Answer 2

Answer:

The radius of the new circle = 31 cm.

Step-by-step explanation:

Given:The circumference of a circle is equal to sum of circumference of two circles with diameters 34 cm and 28 cm.

To find: The radius of new circle.

Solution:

Circumference of a circle is the distance around the boundary of the circle.

Circumference of a circle = 2πr.  Let R be the radius of a new circle and  r₁, r₂ be the radius of other circles.

r₁= 34/2 = 17 cm, r₂ = 28/2 = 14 cm.

given that the circumference of a circle is equal to sum of the circumferences of two circle

⇒ 2πR = 2πr₁ + 2πr₂

⇒ 2πR = 2π(r₁ + r₂)

⇒ 2πR = 2π(17+ 14)

⇒ R = 17+ 14

R = 31.

Therefore the radius of the new circle = 31 cm.