Question

PRACTISE NOW 3
The figure shows a circle of radius 14 cm with one quadrant removed, touching the
sides of a square. Find
(i) the perimeter of the unshaded region,
(ii) the area of the unshaded region,
(iii) the area of the shaded region.
14 cm​

Answer 1

Answer:

perimeter of circle(four quadrants)=2πr

1quadrant =2πr/4

1/2 × πr

so perimeter of 3 quadrants=2πr-1/2πr+r+r

3/2πr+r+r

(note r=radius)

$\frac{3}{2} \times \frac{22}{7} \times 14 + 14 + 14$

$\frac{33}{7} \times 14 + 14 + 14$

(note we can write 14+14 as 2×14)

$33 \times 2 + 2 \times 14$

$66 + 28$

94cm answer(I)

area of unshaded region

Area of circle-1quadrant of cirt

πr²-1/4πr²

22/7 ×14×14 - 1/4×22/7 × 14×14

616-154

462cm² answer (ii)

we see that in the figure length of a side of square=14+14=28cm(means diameter of circle)

so area of square=side×side

28×28=784cm²

(note a circle have four quadrants )

area of circle-1qadrants

=3quadrants

3× 1/4 ×22/7 × 14×14

3/4 × 22×2×14

66/4 ×2×14

33/2 × 2×14

33×14

462cm²

so area of shaded region= area of square-area of 3 quadrants

784-462

322cm² answer (iii)

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