Mensuration

  1. What is the area of a tringle whose sides are 7cm and 9cm ?
    18 √2
    42 √6
    12 √2
    5 √3
    12 √5
    Option E
    S = 7 + 8 + 9/2 = 24/2 = 12
    Area of tringle = √ S(S – a) (S – b) (S – c)
    = √ 12 * 5 * 4 * 3
    = 12 √ 5

     

  2. The perimeter of a square is 96 cm. If the radius of a circle is 3 cm less than the side of that square, then what is area of the circle ?
    1280
    1345
    980
    1045
    1386
    Option E
    perimeter of square = 96cm
    side of square = 96/4 = 24cm
    radius of circle = 24 – 3 = 21 cm
    area of circle = πr^2 = 22/7 * 21 *21 = 1386 cm^2

     

  3. The area of a rectangular field is 252cm^2 and ratio between length and breadth is 9 :7. If cost of wire which is to be fenced is rs.2 per meter, then find cost of fencing the field ?
    240
    340
    130
    145
    128
    Option E
    Let length and breadth are 9x and 7x respectively.
    9x * 7x = 252
    x = 2
    length = 9 * 2 = 18
    breadth = 7 * 2 = 14
    perimeter of rectangular field = 2(18 + 14) = 64m
    cost of fencing wire = 64 * 2 = 128

     

  4. The perimeter of rectangle is 72m and ratio between the length and breadth is 11 : 7. What is the difference between the half of the length and one-seventh of the breadth of rectangle ?
    9m
    6m
    12m
    15m
    17m
    Option A
    Let length and breadth of rectangle 11x and 7x respectively.
    perimeter = 72m
    2(11x + 7x) = 72
    x = 2
    length = 11 * 2 = 22
    breadth = 7 * 2 = 14
    difference = 22/2 – 14 * 1/7 = 11 – 2 = 9m

     

  5. There are two circle A and B and diameter of circle A is equal to be the radius of circle B,. If radius of circle A is 14 cm, Then find the difference between the perimeter of two circle ?
    48cm
    42cm
    154cm
    88cm
    28cm
    Option D
    Radius of circle A = 14 cm
    Diameter of circle A = 14 * 2 = 28
    radius of circle B = 28
    perimeter of circle A = 2 * 22/7 * 14 = 88cm
    perimeter of circle B = 2 * 22/7 * 28 = 176 cm
    difference = 176 – 88 = 88cm

     

  6. Curved surface area of a cylinder is 2640 cm^2 and its height is 20cm. Find the volume of a cylinder.
    27720 cm^2
    4840 cm^2
    22350 cm^2
    32430 cm^2
    16340 cm^2
    Option A
    C.S.A = 2640
    2πrh = 2640
    2 * 22/7 * r * 20 = 2640
    r = 2640 * 7 / 44 * 20 = 21
    volume = πr^2h = 22/7 * 21 * 21 * 20 = 27720 cm^2

     

  7. The length of the rectangle A is 4 m more than the breadth of rectangle and perimeter of rectangle A is 56m. What is the area of rectangle B whose length is equal to the length of rectangle A and breadth is 8 m ?
    64 m^2
    48 m^2
    24 m^2
    128 m^2
    120 m^2
    Option D
    Let breadth of rectangle A = x
    length = x + 4
    perimeter = 56
    2(x + x + 4) = 56
    4x + 8 = 56
    x = 12
    length of rectangle A = 12 + 4 = 16
    length of rectangle B = 16
    breadth = 8
    area = 16 * 8 = 128 m^2

     

  8. A trapezium whose parallel sides are 18 cm and 14 cm long and distance between them ids 9cm. What is the area of trapezium ?
    158 cm^2
    240 cm^2
    144 cm^2
    152 cm^2
    245 cm^2
    Option C
    Area of trapezium = 1/2 * (18 + 14) * 9 = 144 cm ^2

     

  9. If the ratio of two curved surface area of two cylinder A and B are 4 : 5 and ratio of their radius is 2 : 1, then what is the ratio of their volumes ?
    8 : 7
    9 : 10
    13 : 7
    8 : 5
    3 : 4
    Option D
    Let radius of cylinder A and B = r_1 and r_2
    height cylinder A and B = h_1 and h_2
    2πr_1 h_1 / 2πr_2 h_2 = 4/5
    h_1 / h_2 * 2/1 = 4/5
    h_1 / h_2 = 2/5
    ratio of their volumes = π^2r_1 h_1 / π^2r_2 h_2
    (2)^2 * 2 / (1)^2 * 5 = 8/5

     

  10. If the radius of cone is increased by 50% and height is decreased by 40%, then find the percentage change in the volume ?
    55% decrease
    40% increase
    45% decrease
    48% increase
    50% decrease
    Option A
    Let radius of cone = 100
    after increased radius of cone = 100 + 50 = 150
    ratio = 2 : 3
    let height of cone = 100
    after decreased radius of cone = 100 – 40 = 60
    ratio = 5 : 3
    volume = 1/3 * πr^2h = 1/3 * 22/7 * 4 * 5 = 440 / 21
    volume = 1/3 * πr^2h = 1/3 * 22/7 * 3 * 3 = 198/21
    decrease = 242 / 440 * 100 = 55%

     


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