Question

Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm and 18 cm.​

Answer 1

Step: Finding the diameter of circle

Assume that the radius of required circle = 𝑟

Circumference of circle = $2\pi r$

For first circle, radius = 10 cm

Circumference of first circle $=2\pi \left(10\right)cm$

For second circle, radius = 12 cm

The circumference second circle = $2\pi \left(12\right)cm$

For third circle, radius = 18 cm

The circumference of third circle = $2\pi \left(18\right)cm$

Now, $2\pi r=2\pi \left(10\right)+2\pi \left(12\right)+2\pi \left(18\right)$

$\Rightarrow r=10+12+18=40cm$
$\therefore$ Diameter $=2r=2\times 40=80cm$

Hence, diameter of required circle = 80 cm