Question

Solve the problems
area realated to circle​

Answer 1

Question

From each centre of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in fig. Find the area of remaining portion of the square.

Answer

16 - 2π cm² or 9.72 cm² (approx)

Explanation

Since there are four quadrants of same radius (1 cm), they together will form a complete circle with radius 1 cm

And, the circle in the centre has a diameter 2 cm.

→ radius of circle in the centre = 1 cm.

So, area of remaining portion = area of square - area of 4 quadrants - area of circle in the centre

Area of square = side² = 4² = 16 cm²

area of 4 quadrants = area of complete circle formed by them = πr² = π(1)² = π cm²

Area of circle in the centre = πr² = π(1)² = π cm²

So, area of remaining portion = 16 - π - π

= 16 - 2π cm²

Now, taking π as 3.14, we get

16 - 2(3.14) cm²

= 16 - 6.28 cm²

= 9.72 cm²

Answer 2

Given:

A square with sides 4 cm

4 quadrants with radius of 1 cm at the corner cut out

A circle with diameter in the middle cut out

To Find:

Shaded Region of the square

Find the area of the square:

$\text {Area of the square} = \text{Lenght} \times \text{Length}$

$\text {Area of the square} = \text{4} \times \text{4}$

$\text {Area of the square} = \text{16 cm}^2$

Find the area of the 4 quadrants:

$\text{Area of the 4 quadrants} = 4 \bigg( \cfrac{1}{4} \times \pi r^2 \bigg)$

$\text{Area of the 4 quadrants} = 4 \bigg( \cfrac{1}{4} \times \pi (1)^2 \bigg)$

$\text{Area of the 4 quadrants} = \pi \text{ cm}^2$

Find the area of the circle in the middle:

$\text{Area of a circle} = \pi r^2$

$\text{Area of the circle} = \pi (2 \div 2)^2$

$\text{Area of the circle} = \pi \text{ cm}^2$

Find the area of the shaded part:

$\text{Area of the shaded part} = 16 - \pi - \pi$

$\text{Area of the shaded part} = 16 - 2\pi$

$\text{Area of the shaded part} = 9\dfrac{5}{7} \text{ cm}^2$

$\text {Answer} =9\dfrac{5}{7} \text{ cm}^2$