Question

Find the radius of the circle whose circumference is equal to the sum of circumferences of two circles whose diameter are 10 cm and 20 cm.

Answer 1

Answer:

The radius of the circle is 15/π cm

Step-by-step explanation:

The sum of the circumferences of the two circles = 10cm + 20cm = 30cm

Thus, the circumference of the given circle = 30cm

Let r be the radius of the required circle. Therefore,

Circumference of the required circle = 2πr

Circumference = πd (where d = 2r = diameter)

Thus, πd = 30

d = 30/π

2r = 30/π

r = 15/π

Answer 2

Answer:

Radius of the Circle = 15 cm

Step-by-step explanation:

1. Circumferences of the other two circles:

   $2*\pi *5=10\pi \\2*\pi *10=20\pi$

2. Sum the two Circumferences to find the circumference of the big circle:

   $10\pi +20\pi =30\pi$

3. Find the radius:

   $30\pi =2*\pi *r$

   $\frac{30\pi }{\pi } =2r$

   $\frac{30}{2}=r$

   $r=15 cm$