Question

Find theta and hence the shaded area when:
a) AB = 10 cm, r = 10 cm
b) AB = 8 cm, r = 5 cm​

Answer 1

Answer:

a) angle of sector =

$\pi \times {r}^{2} \times \frac{theta}{360 }$

$\frac{22}{7} \times 10 \times 10 \times \frac{theta}{360}$

$\frac{22}{7} \times 5 \times 1 \times \frac{theta}{18}$

$\frac{11}{7} \times 5 \times 1 \times \frac{theta}{9}$

$\frac{55}{7} \times \frac{theta}{9}$

$\frac{55theta}{63}$

55 theta

theta = 55

Area of shaded region =

$\pi \times {r}^{2} \times \frac{theta}{360} - \frac{ {r}^{2} }{2} \times \sin(theta)$

$\frac{22}{7} \times 10 \times 10 \times \frac{55}{360} - \frac{10 \times 10}{2} \times \sin(55)$

$\frac{11}{7} \times 5 \times 5 \times \frac{11}{9} - 10 \times \sin(55)$

$\frac{3025}{63} - 10 \times \sin(55)$

$\frac{3025 - 630}{63} \times \sin(55)$

$\frac{2395}{63} \times \sin(55)$

38.01 × sin(90-55)

38.01 × sin (45)

38.01 × 1/√2

38.01/√2

26.877

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Answer 2

Answer:
theta for part a) 90 degrees

Shaded area part a)  9.06    

Step-by-step explanation:

theta :
MB= 5cm
Sin inverse = 5/10
                   = 30
theta = 30 x 2
theta= 60

shaded area:
Area of sector - area of triangle

$\frac{theta}{360} * pi*r^2\\\frac{60}{360} *pi*10^2\\= 52.35$

triangle area:
1/2 *10 * 10* sin 60
= 43.30

52.35-43.30
=9.6