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Question 22 Mensuration Exercise 16.3

In the figure (i) given below, a chord AB of a circle of radius 10 cm subtends a right angle at the centre

O. Find the area of the sector OACB and of the major segment. Take π = 3.14.

Answer:

It is given that

The radius of the circle = 10 cm

The angle at the center subtended by a chord AB = 90^{\circ}

We know that

Area of sector OACB = πr

2

× 90/360

Substituting the values

= 3.14 × 10 × 10 × 90/360

So we get

= 314 × ¼

"hello and welcome my dear students i'm
richard purana the maths you don't know
lido
and i'm here with a new question it says
in the figure 1 given below
a chord a b of a circle of radius 10
centimeter
subtends a right angle at the center
o find the area of the sector oacb and
of the major segment
take pi as 3.14 so be careful while
solving the question
so without wasting much time let's have
a look at the solution
so it is given that the radius of the
circle is 10
so i'm writing radius for that
the radius the angle of this intercept
ended by the chord a b
it's 90 degree we know that
area sector
oacb is equals to
pi r square into 90 upon 360.
which is nothing but equals to 3.14
into one by four so solving this
we get
c so the radius given as 10
so be careful that you also put the
values of the radius
which is 1 by 4 so now solving this you
get 1 by 4 which is nothing but
78.5
centimeter square
so hence the area of oacb is the
78.5 centimeter square
right now let's find out the area of
triangle oab
half into base into height which is half
into 10 into 10
being the radius which is 50 centimeter
square
now the area of the minus segment
is equals to area sector
oacb minus
area of triangle oab
which is nothing but equals to 78.5
minus 50 which is nothing but equals to
28.5
centimeter square
also the area of circle
is pi r square this we all know and pi
is 3.14 into radius being 10
so this is equal to 314 centimeter
square
now hence we need to find out the age of
major segment
so let's look at that so area of major
segment
is equals to area of circle
minus area of minus segment
which is nothing but equals to 314
minus 28.5
which is nothing but equals to 285.5
centimeter square
so i hope my students got this question
well do not forget to hit the subscribe
button
you can also share your doubts in the
comment section see you next time bye"

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