A square ABCD is inscribed in a circle of unit radius. Semi-circl

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111.

A square ABCD is inscribed in a circle of unit radius. Semi-circles are described on each side as a diameter. The area of the region bounded by the four semi-circles and the circle is

  • 1 sq unit

  • 2 sq unit

  • 1.5 sq unit

  • 2.5 sq unit


B.

2 sq unit


As square is inscribed in a circle therefore, 
 Side space of space square space left parenthesis straight a right parenthesis equals space square root of 2 straight r
rightwards double arrow space space space space straight a space equals space square root of 2 space cross times space 1 space equals space square root of 2 space unit
As, Diameter of Semi circle is the side of square, 
∴  Radius of semi circle  = fraction numerator square root of 2 over denominator 2 end fraction space equals space fraction numerator 1 over denominator square root of 2 end fraction
∴  Area of one-semi circle:
           straight pi over 2 open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared space equals space straight pi over 4 space sq space unit
Area of 4-semi circle:
                 equals space 4 space cross times space straight pi over 4 space equals space straight pi space space space space space... left parenthesis straight i right parenthesis
Area bounded by region
      =  Area of circle  - Area of square
       equals space straight pi left parenthesis 1 right parenthesis squared space minus space left parenthesis square root of 2 right parenthesis squared
equals space straight pi space minus space 2 space space space space space space space... left parenthesis ii right parenthesis
Hence, Required area bounded by four semi-circles  = (i) - (ii)
                          equals space straight pi space minus space straight pi space plus space 2 space equals space 2 space sq space unit

                     

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112.

The sides of a triangle having area 7776 sq cm are in the ratio 3 : 4 : 5. The Perimeter of the triangle is

  • 412 cm

  • 424 cm

  • 400 cm

  • 432 cm


113.

If the area of a circle is A, radius of the circle is r and circumference of it is C, then

  • rC = 2A

  • straight A over straight r space equals space straight C

  • AC space equals space straight r squared over 4

  • straight C over straight A space equals space straight r over 2


114.

The perimeter of one face of a cube is 20 cm. Its volume will be

  • 400 cm3

  • 125 cm3

  • 625 cm3

  • 100 cm3


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115.

A solid sphere of diameter 17.5 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area?

  • 289 cm2

  • 361.5 cm2

  • 481.25 cm2

  • 962.5 cm2


116.

What is the area (in cm2) of a rectangle if its diagonal is 25 cm and one of its sides is 24 cm?

  • 186 cm2

  • 144 cm2

  • 132 cm2

  • 168 cm2


117.

Area of 4 walls of a cuboid is 57m2, if its length is 5.5 m and height is 3 m. What is the breadth (in m)?

  • 4.5 m

  • 4 m

  • 3 m

  • 3.5 m


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