Question

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

Answer 1

Answer:-

Given:

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.

Answer 2

Answer:

✡ Given ✡

$\leadsto$ A circle whose area is 4 times area of a circle with diameter 21 cm.

✡ To Find ✡

$\leadsto$ What is the circumference of a circle.

✡ Solution ✡

✏ Diameter = 21 cm

✏ So, radius = $\dfrac{21}{2}$ cm = 10.5 cm

So, area of the circle = πr²

$\implies$ $\dfrac{22}{7}$ × (10.5)²

$\implies$ 346.5 cm²

So, area of second circle is 4 times 346.5 cm²

Then, area is,

$\implies$ 4 × 346.5 cm²

$\implies$ 1386 cm²

Therefore,

$\implies$ $\dfrac{22}{7}$ × r² = 1386

$\implies$ r² = 1386 × $\dfrac{7}{22}$

$\implies$ r² = 441

$\implies$ r = $\sqrt{441}$

$\implies$ r = 21 cm

So, radius of the first circle = 21 cm

Then, the circumference = 2πr

$\implies$ 2 × $\dfrac{22}{7}$ × 21

$\implies$ 132 cm

Hence, the circumference of the circle is 132 cm.

Step-by-step explanation:

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