Latest TCS Aptitude Question SOLUTION: a semicircle is drawn with AB as its diameter. from C a point on AB,a line parpendicular to AB is drawn,meeting the circumference of the semicircle at D. Given that AC=2 and CD=6,t

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a semicircle is drawn with AB as its diameter. from C a point on AB,a line parpendicular to AB is drawn,meeting the circumference of the semicircle at D. Given that AC=2 and CD=6,the area of the semicircle is?

Asked In TCS Neerajita pal (9 years ago)

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Sourav ganguly  (9 years ago)

Draw a semicircle with M as a centre(say) and AB is the diameter,therefore,AM=MB=r(say,radius of the semicircle)
Also,draw perpendicular DC on AB such that,CD=6 cm,AC= 2cm
so, CM= AM-AC=r-2.also join M and D and MD= r
In triangle MCD,by pythagoras theorem
MD^2=CM^2 + CD^2
r^2 = (r-2)^2 + 6^2
r^2 = r^2 + 4 -4r + 36
so, r= 10 cm

therefore area of semicircle =1/2*pi*(r^2)
=1/2*pi*(10^2) =50 pi

Is this solution Helpfull? Yes (41) | No (1)  

manish  (9 years ago)

radius of circle will be 10 because sq(r-2)+sq(6)=sq(r)
then area of semi circle will be 3.14*10*10/2=50pie

Is this solution Helpfull? Yes (4) | No   

Vaibhav  (9 years ago)

Let mid point of AB be E
AE=r radius of semicircle
Given D is the point on circum of circle
Then ED = radius of semicircle r
Let C be the point lie in b/w AE
CD perpendicular to AB
CD = 6cm given
AC = 2cm given
then CE = r-2
From the rt angle triangle DCE
r^2=36+(r-2)^2
On solving we get r=10
Area of semicircle = (1/2)(pi)(r)^2



= 50pi answer

Is this solution Helpfull? Yes (3) | No   

razi  (9 years ago)

Draw a semicircle with M as a centre(say) and AB is the diameter,therefore,AM=MB=r(say,radius of the semicircle)
Also,draw perpendicular DC on AB such that,CD=6 cm,AC= 2cm
so, CM= AM-AC=r-2.also join M and D and MD= r
In triangle MCD,by pythagoras theorem
MD^2=CM^2 + CD^2
r^2 = (r-2)^2 + 6^2
r^2 = r^2 + 4 -4r + 36
so, r= 10 cm

therefore area of semicircle =1/2*pi*(r^2)
=1/2*pi*(10^2) =50 pi

Hope you are clear with the soluion

Is this solution Helpfull? Yes (1) | No   

Ridhita  (9 years ago)

ans is 20pie

Is this solution Helpfull? Yes | No (2)  

Aravind Kumar  (9 years ago)

aravindarjun48@gmail.com

Is this solution Helpfull? Yes | No   

Rajanikanta Pradhan  (8 years ago)

Ans is 50pi

Is this solution Helpfull? Yes | No (1)  

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