Question

The area of a circle is 3850. find the area of a square inscribed in the circle​

Answer 1

Answer:

Step-by-step explanation:

Given that,

The area of the circle = a = 3850sq cm.

∴ a = πr²

⇒ 3850 = 22/7 × r²

⇒ r² = 3850 × 7 / 22

⇒ r² = 1225

⇒ r = √1225

⇒ r = 35 cm.

∴ The area of a square inscribed in the circle = 2r² = 2 × 35 × 35 = 2450 sq cm

Answer 2

Given:

The circle has an area of 3850 cm²

To find:

The area of the inscribed square.

Solution:

We know that area of a circle is,

Area of circle = $\pi$ R²

3850 = $\pi$ R²

R²= 3850/$\pi$

Value of $\pi$ = 22/7

R= √1225

R = 35 cm

Diameter of circle = 2×R = 70 cm

Now, the circle has a square inscribed inside it.  The diameter of the given circle becomes the diagonal of the inscribed square.

The length of the diagonal of the square is equal to the circle’s diameter.

That is,

Diagonal (D) = 70 cm.

When the length of the diagonal of a square is present, then the side of the given square is,

Side = D /√2

Hence, the length of the side of the square = D /√2 = 70/√2 cm

= 49.49 cm

Now

Area of the square = (Side)² square units

Area of the inscribed square = (49.49)² cm²

Area = 2449.26 cm²

The area of the square inscribed inside the circle is 2449.26 cm²