Question

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


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Answer 1

Answer:

Area of square = (4)² = 16 cm²

Area of circle = 22/7 × (1)² = π cm²

Remaining area = (16-π) cm²

Answer 2

Answer:

$\bf \fbox \red{ Area of the shaded region is 68/7 cm²}$

Step-by-step explanation:

Side of square = 4 cm

Radius of quadrant of circle = 1 cm = R1

There are 4 quadrants of a circle with radius 1 cm.

Therefore;

$Area \: of \: 4 \: quadrant = 4 \times \frac{1}{4} \pi \: {r}^{2} \\ \\ = \frac{22}{7} \times 1 \times 1 \\ \\ = \frac{22}{7} {cm}^{2}$

$Area \: of \: circle \: of \: diameter \: 2 cm = \pi \times {( \frac{d}{2} )}^{2} \\ \\ = \frac{22}{7} \times \frac{2}{2} \times \frac{2}{2} \\ \\ = \frac{22}{7} \: {cm}^{2}$

$Area \: of \: Total \: area \: of \: unshaded \: region = \frac{22}{7} + \frac{22}{7} \\ \\ = \frac{44}{7} \: {cm}^{2}$

$Area \: of \: square = {side}^{2} \\ \\ = 4 \times 4 \\ \\ = 16 \: cm$

$Area \: of \: th e \: shaded \: region = 16 - \frac{44}{7} \\ \\ = \frac{112 - 44}{7 } \\ \\ = \frac{68}{7} \: {cm}^{2}$

$\bf \fbox \green { Hence ,Area of the shaded region is 68/7 cm²}$