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Aptitude miscellaneous
  1. The ratio of the area of the in-circle and the circum-circle of a square is








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,

    Let the side of the square be 2x. Then radius of incircle = a Radius of circum-circle
    √a² + a² = √2a
    ∴ Ratio of area = πa² : π(√2a)² = a² : 2a² = 1 : 2

    Correct Option: A

    Using Rule 14,

    Let the side of the square be 2x. Then radius of incircle = a Radius of circum-circle
    √a² + a² = √2a
    ∴ Ratio of area = πa² : π(√2a)² = a² : 2a² = 1 : 2

  1. The perimeter of a semicircular path is 36 m. Find the area of this semicircular path.








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,
    πr + 2r = 36

    ⇒ r
    22
    		 + 2 = 36
    7

    ⇒ r
    22 + 14
    		 = 36
    7

    ⇒ r =
    36 × 7
    		 = 7 metre
    36

    Area =
    πr²
    2

    =
    1
    		 ×
    22
    		 × 7 × 7
    27

    = 77 sq. metre

    Correct Option: D

    Using Rule 14,
    πr + 2r = 36

    ⇒ r
    22
    		 + 2 = 36
    7

    ⇒ r
    22 + 14
    		 = 36
    7

    ⇒ r =
    36 × 7
    		 = 7 metre
    36

    Area =
    πr²
    2

    =
    1
    		 ×
    22
    		 × 7 × 7
    27

    = 77 sq. metre

  1. The ratio between the area of two circles is 4 : 7. What will be the ratio of their radii?








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,
    πr1² : π2² = 4 : 7
    ⇒ r1 : r2 : √4 : √7 = 2 : √7

    Correct Option: A

    Using Rule 14,
    πr1² : π2² = 4 : 7
    ⇒ r1 : r2 : √4 : √7 = 2 : √7

  1. Three circles of radius a, b, c touch each other externally. The area of the triangle formed by joining their centre is








  1. View Hint View Answer Discuss in Forum

    Using Rule 1,

    x = AB = a + b
    y = BC = b + c
    z = CA = a + c

    ∴ s =
    AB + BC + CA
    		 = a + b + c
    2

    ∴ Area of ∆ ABC
    = √s(s - x)(s - y)(s - z)
    = √(a + b + c)abc

    Correct Option: A

    Using Rule 1,

    x = AB = a + b
    y = BC = b + c
    z = CA = a + c

    ∴ s =
    AB + BC + CA
    		 = a + b + c
    2

    ∴ Area of ∆ ABC
    = √s(s - x)(s - y)(s - z)
    = √(a + b + c)abc

  1. The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. Find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).








  1. View Hint View Answer Discuss in Forum

    Using Rule 14,

    Area of circle = kr²
    Area of shaded region
    = k (5² – 3²) = 16π sq. units
    Area of larger circle = k × 5²
    = 25p sq. units
    ∴ Required ratio = 16 : 25

    Correct Option: C

    Using Rule 14,

    Area of circle = kr²
    Area of shaded region
    = k (5² – 3²) = 16π sq. units
    Area of larger circle = k × 5²
    = 25p sq. units
    ∴ Required ratio = 16 : 25