Question

Find the area of a circle inscribed in a square of area 441 sq.cm

Answer 1

Step-by-step explanation:

Side of square will be equal to the diameter of circle. So the radius of circle is half of 441 i.e. 220.5cm.

area of circle =πr^2

22/7×220.5×220.5

152,806.5sq.cm

area of square=441×441

194,481sq.cm

Area of enclosed part is area of square minus area of circle. =194,481-152806.5

=41,674.5sq.cm

Answer 2

Area of the circle is 346.5 cm²

Given:

A circle is inscribed square

Area of the square = 441 sq.cm

To find:

Area of the circle

Solution:

When a circle inscribed in a square the length side will be equals to the diameter of the circle

To find the diameter of the circle we need to know length of the square  

From given data area of the square = 441 sq.cm

As we know area of the square = side²

⇒ side² = 441 sq.cm

⇒ side² = 21² cm    [ ∵ 441 = 21 × 21 ]

The length of the side = 21 cm

⇒ diameter of the circle 2r = 21 cm

⇒ Radius of the circle = 21/2 = 10.5 cm

Area of the circle = πr²

= $(\frac{22}{7} )(10.5)^{2}$ =  (3.1428) (110.25) = 346.5 cm²  

Area of the circle = 346.5 cm²

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