Find the the circumference of a circle whose area is 4 times area of a circle with diameter 21 CM

Diameter of a circle = 21 cm.

Area of other circle = 4 * area of the circle

circumference of a circle

Diameter of a circle = 21 cm.

→ Radius of the circle = 21/2 cm

And,

Area of other circle = 4 * area of the circle.

We know that,

Area of a circle with radius r is :

→ πr²

Let the radius of the given circle be r₁ and radius of the other circle be r₂

Hence,

→ π * (r₂)² = 4 * π * (r₁)²

Putting the value of r₁ and cancelling π from both sides we get,

→ (r₂)² = 4 * (21/2)²

→ (r₂)² = 4 * (21)²/4

→ (r₂)² = (21)² cm

→ r₂ = 21 cm

[If powers are equal, then the bases are also equal ]

Now,

Circumference of a circle = 2πr

→ Circumference of the other circle = 2 * π * r₂

→ Circumference of the other circle = 2 * 22/7 * 21

→ Circumference of the other circle = 132 cm

Hence, the circumference of the other circle is 132 cm.

I hope it will help you.

Regards.

π * (r₂)² = 4 * π * (r₁)²

Putting the value of r₁ and cancelling π from both sides we get,

 (r₂)² = 4 * (21/2)²

 (r₂)² = 4 * (21)²/4

 (r₂)² = (21)² cm

 r₂ = 21 cm

Circumference of a circle = 2πr

Circumference of the other circle = 2 * π * r₂

Circumference of the other circle = 2 * 22/7 * 21

Circumference of the other circle = 132 cm