Question

From the four corners of a square piece of paper of side 24cm quadrants with centres at the vertices of the square are cut off .if the radius of each quadrant is 7 cm find the area of paper left

Answer 1

Answer:

Area of square =4×4=16cm

2

Area of sector =

360

θ

×π×r

2

Area of 4 quadrants =4×

360

90

×π×1×1

=3.14cm

2

Area of circle=π×r

2

=π×1×1

=3.14cm

2

∴ Area of shaded region =16−6.28 =9.72cm

2

Answer 2

Answer:

Area left off = 422cm²

Step-by-step explanation:

Let s be the side of this square

then, s = 24cm (given)

Now, each Quadrant is cut off keeping the vertices as its centre

so, it forms a Sector of 90°

But here a Quadrant is formed, that is, (1/4) of the circle is called Quadrants

Thus, 1 Quadrant's area = (1/4) × πr²

= (πr²)/4

Now, from this square piece four quadrants are cut off

so, total area = ((πr²)/4) + ((πr²)/4) + ((πr²)/4) + ((πr²)/4)

= 4((πr²)/4) = πr²

Because, see 4 Quadrants make up one circle, here also we are using 4 Quadrants

Now,

area left off = area of square - area of circle

Area of a square = s²

= 24² = 576cm²

Area of Circle = πr²

= π × 7²

Using π = (22/7) we get

Area = (22/7) × 7 × 7 = 22 × 7 = 154cm²

so, Area left off = 576 - 154 = 422cm²

Thus, 422cm² is left out

Hope it helped and you understood it........All the best