M4maths Previous Puzzles

19 May 2015 Area of the disc

From a circular disc of radius 10 cm, a rectangle of maximum area is cut. Area of the remaining disc will be

OPtion

1) 98 cm^2
2) 99 cm^2
3) 103 cm^2
4) 107 cm^2
5) 109 cm^2
6) 111 cm^2
7) 114 cm^2
8) 119 cm^2
9) 121 cm^2
10)124 cm^2

Solution

Area of circular disc = Pi*(10 cm)^2
= 100 Pi
314 cm^2
Now rectangle of maximum area inside circle will be square of side length r*Sqrt2, where r is radius so
Area of square disc = (r*Sqrt2)^2
= 2r^2 = 2*(10cm)^2
= 200 cm^2
So area of remaining disc = 314-200 cm^2
114 cm^2
Option 7)

Correct Option: 7 Best Solution (17)

siddharth prakash singh   10 years AGO

for max area rectangle inside the circle will be a square. whose diagonal will be the diameter of circle.
so diagonal of circle= 20 cm.
side of square=20/sqrt2.
so rem area= 100pi-(20/sqrt2.)^2=114 cm^2

Like? Yes (3) | No (1)  

Devendra Marghade   10 years AGO

A rectangle of maximum area will be the square whose diagonal=Diameter of Circle=2*10=20 cm.
If a side of a square=x cm. then x^2+ x^2=20^2
On solving, x=10Sqrt(2)
So area of rectangle=[10Sqrt(2)]^2=200 cm^2
Area of remaining disc=Pi*r^2 -200
=3.14*10^2 -200=114
So answer is option (7)

Like? Yes (3) | No (1)  

RAKESH   10 years AGO

100*pi - (10*sqrt2)^2 = 114 cm^2

Like? Yes (4) | No (3)  

MD SOHAIL AKHTER   10 years AGO

area of circle= 314 cm^2
area of max rectangle= area of square with diagonal as circle's diameter =200 cm^2
area of rem. parts= 114cm^2

Like? Yes (2) | No (1)  

sompon temtheerakij   10 years AGO

area of disc = 3.14*10*10 = 314 cm^2
area of rectangle = sq root of 200 * sq root of 200 = 200 cm^2
Area of the remaining disc = 14-200 = 114 cm^2

Like? Yes (1) | No   

sravani   10 years AGO

pi*10^2 - (10sqrt(2))^2 =114.28

Like? Yes (2) | No (1)  

ravi singh   10 years AGO

Area of remaining
disc =pi*r^2 - 2r^2
=(pi-2)*r^2
=(3.14-2)*100
=114 cm^2

Like? Yes (2) | No (1)  

umesh   10 years AGO

area of max rectangle is 200
area of circular disc is 314
so remain area is 114

Like? Yes (2) | No (1)  

vivek   10 years AGO

as maximum area must be a square.
remaining area = area of the circle-area of square
so, area = 3.14*10*10-(1/2*20*20)=314-200=114

Like? Yes (2) | No (1)  

Surit Datta   10 years AGO

Let h be the height and w be the width of an inscribed rectangle.
The area then is given by A = w*h.
By drawing in the diagonal of the rectangle, which has length 10 cm, we obtain the relationship ,
w^2 + h^2 = 400
so,
A = h * sqrt(400 - h^2), 0

Like? Yes (3) | No (2)  

Karthick Raja   10 years AGO

a rectangle of maximum area is cut in a circle is square so diagonal of square is 20 cm
1.414*a = 20
a=14.14 cm
area of rectangle (square)=14.14*14.14=200 cm^2
area of circle = 3.14*10*10=314 cm^2
Area of the remaining disc will be =314-200 = 114 cm^2

Like? Yes (2) | No (1)  

Sushil Singh   10 years AGO

first find the area of one chord using given details
now multiply it with 4 to get remaining area of circle.
here ans is 114 cm^2

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suraj nath prasad   10 years AGO

max area can be obtained when it is a square

Like? Yes (2) | No (1)  

shikha KUMARI   10 years AGO

first take the area of disc (pi*r*r)= pi*10*10=100*22/7=2200/7
then area of rectangle l*b
length= diameter of disc=20cm
breadth= 5cm upper side from centre and 5cm lower side from centre= 10cm
area= 20*10=200cm
then substract the area of rectangle from the area of disc
2200/7-200=114cm^2

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aman aditya   10 years AGO

area of circle:3.14*10*10=314
area of rectangle=10root2*10root2=200
area left=114

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Aditi Tenguria   10 years AGO

AREA OF MAXIMUM AREA OF RECTANGLE MEANS A SQUARE IS CUT;
side of square=10*(2)pow1/2

AREA OF REMAINING DISC= AREA OF DISC-AREA OF SQUARE
=>22/7*10*10 -200
=>114.28 sq.cm

Like? Yes (2) | No (3)  

Nitish Kumar Dubey   10 years AGO

The radius is 10 then from there we get side of square by aplying pytha goras theorem. a=10 sqrroot2

Area Of square= 200.

Area of circle= 314

Reamaining Area= 314-200= 114

Like? Yes (1) | No (2)