A chord of a circle radius 10 cm subtends a right at the centre find the area of the corresponding.
i) minor segment
ii)major segment
Answers
ANSWER
(i) Area of minor segment (shaded region) = Area of the quadrant AOB− Area of the △AOB
=41×πr2−21×AO×OB
=41×3.14×(10 cm)2−21×10 cm×10 cm
=41×3.14×100 cm2−50 cm2
=78.5 cm2−50 cm2
=28.5 cm2
(ii) Area of the major segment = Area of the circle − Area of the minor segment
=πr2−28.5 cm2
=3.14×(10 cm)2−28.5 cm2
=314 cm2−28.5 cm2
=285.5 cm2
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( use 3.14)
10th
Maths
Areas Related to Circles
Area of Segment
A chord of a circle of radi...
MATHS
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use π=3.14)
ANSWER
(i) Area of minor segment (shaded region) = Area of the quadrant AOB− Area of the △AOB
=
4
1
×πr
2
−
2
1
×AO×OB
=
4
1
×3.14×(10 cm)
2
−
2
1
×10 cm×10 cm
=
4
1
×3.14×100 cm
2
−50 cm
2
=78.5 cm
2
−50 cm
2
=28.5 cm
2
2) part (ii) Area of the major segment = Area of the circle − Area of the minor segment
=πr
2
−28.5 cm
2
=3.14×(10 cm)
2
−28.5 cm
2
=314 cm
2
−28.5 cm
2
=285.5 cm
2
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