The diagram shows a sector of a circle with centre O and radius 6cm. MN is a chord of the circle.
Angle MON is 50°

calculate the area of the shaded segment.
give your answer to 3 significant figures

Step-by-step explanation:

Area of the shaded segment = area of the sector OMN - Area of the triangle OMN

Area of the sector OMN =

r= radius of the sector

= angle substended by the sector

Area of the sector OMN

Area of triangle ABC =

To get the height, we will use SOH CAH TOA trigonometry identity

According to SOH;

sin 25° = opp/6

opp = 6sin25°

opp = 2.54cm

The base of the triangle = 2(2.54) = 5.08cm

Th height can be gotten using the pythagoras theorem. The hypotenuse = 6cm and the opposite = 2.54cm

the adjacent = height = 5.44cm

Area of the triangle OMN

Area of the shaded region = 15.71-13.82

Area of the shaded region = 1.89cm² to 3sf

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls