Question

The circumference of a circle is equal to the sum of the circumference of two circles having diameters 36 cm and 20 cm. The radius of the new circle is

Options

• 16 cm

• 28 cm

• 42 cm

• 56 cm

Answer 1

28 cm

Let r cm be the radius of the new circle.

We know:

Circumference of the new circle = Circumference of the circle with diameter 36 cm + Circumference of the circle with diameter 20 cm

Thus, we have:

2πr = 2πr + 2πr₂ 

⇒ 2πr = (2π × 18) + (2π × 10)

⇒ 2πr = 2π × (18 + 10)

⇒ 2πr = (2πr × 28 )

`⇒ 2πr =( 2 × 22/7xx28)`

⇒ 2πr = 176

`⇒ 2 × 22/7xx"r"=176`

`=> "r" = (176xx7/44)`

⇒ r =28 cm