A sector of circle of radius equal to one fourth of the diagonal of square is cut from the square

M4maths Previous Puzzles

18 Nov 2009 AREA

A sector of circle of radius equal to one fourth of the diagonal of square is cut from the square
taking one corner of the square as centre. If side of the square is 4 cm. then area of the remaining part is

OPtion

1) 15.68
2) 14.43
3) 12.78
4) 10.34
5) 14.73
6) 13.14
7) 14.14
8) 11.88
9) 11.83
10) 9.83

Solution

Diagonal of the square = 4√2 cm.
Hence radius of the circle = 4√2/4 cm. = √2 cm.
Area of the sector of circle = 1/4 (π* radius2)
= 1/4 (π* (√2)2 )
= π/2
Area of the square = 4*4 = =16 cm.2
Hence area of remaining part = 16- (π/2) cm.2

Correct Option: 2 Best Solution (5)

Dr.Dipin Singh   14 years AGO

Area of square = 16 sq cm.

Length of diagonal of Square = Sq Root ( 16+16)= 4 root 2 cm

Radius of sector circle = 1/4 of Length of diagonal of Square = root 4 cm

Area of sector =( 1/4 )*(22/7) * ( root2)^2

= 22/14 sq cm= 1.57 sq cm

Area of remaining portion = 16- 1.57= 14.43 sq cm

option 2

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Bimal   14 years AGO

Area of sq - 1/4 area of circle
( of rad=(root 32)/4)
= 16- 1.57= 14.43 sq cm

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Sukham   14 years AGO

Area of sq=16 sq cm
Rad of circle= Sq root 32
Area of 1/4 circle = 1.57 sq cm

Area of remaining part = 16-1.57 =14.43 sq cm

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Arneet   14 years AGO

Area of sq - area of sector = 16-1.57 = 14.43 sq cm

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SURAJ   14 years AGO

Area of Square = 4 * 4 = 16
Area of Sector = (1/4) * 3.14 * 2 = 1.57
Area of Remaining part = 16 - 1.57 = 14.43

Like? Yes (1) | No