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Mensuration Test 11
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Mensuration Test 11
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  • Question 1/20
    1 / -0

    A slice from a circular pizza of diameter 14 inches is cut in a such a way that each slice of pizza has a central angle of 45°. What is the area of each slice of Pizza(in square inches)?

    Solutions

    Explanation :

    D = 14

    R = D/2 = 14/2 =7

    Area of each slice of Pizza =πr² * Θ/360°

    = (22/7) * 7 * 7 * (45°/360°)

    =19.25

     

  • Question 2/20
    1 / -0

    A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?

    Solutions

    Explanation :

    378 = 2 * 3 * 3 * 3 * 7

    525 = 3 * 5 * 5 * 7

    Highest Common Factor(HCF) = 3 * 7 = 21

    Size of largest tile = 0.21 m by 0.21 m

    Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450

     

  • Question 3/20
    1 / -0

    Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 784 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?

    Solutions

    Explanation :

    Area = 784 cm²

    a = 28 cm

    Perimeter of Square = 4 * 28

    Circumference of a Circle = 4 * 28 * 22/7

    2πr = 4 * 4 * 22

    r = 16 * 22 * 7 / 2 * 22 = 56 cm

    Radius of Circle B = 56/4 = 14 cm

    Area of Circle = πr² = 22/7 * 14 * 14 = 616 cm²

     

  • Question 4/20
    1 / -0

    The area of a rectangle is equal to the area of a square whose diagonal is 12√6 metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).

    Solutions

    Explanation :

    d = a√2

    12√6 = a√2

    a = 12√3

    l * b = a² = (12√3)² = 432

    l – b = 6 ; l = b + 6

    (b + 6)*(b) = 432

    b² + 6b – 432 = 0

    b = 18; l = 24

    2(l + b) = 2(24 + 18) = 84m

     

  • Question 5/20
    1 / -0

    The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.

    Solutions

    Explanation :

    Length = x; Breadth =y

    xy – (x-5)(y+3) = 9

    3x – 5y – 6 = 0 —(i)

    (x+3)(y+2) – xy = 67

    2x + 3y -61 = 0 —(ii)

    solving (i) and (ii)

    x = 17m ; y = 9m

     

  • Question 6/20
    1 / -0

    Height of a cylindrical jar is decreased by 36%. By what percent must the radius be increased, so that there is no change in its volume?

    Solutions

    Explanation :

    volume of cylindrical jar = Πr1²h

    volume of cylindrical jar = Πr2²(64/100)*h = (16/25)*Πr2²h

    r2²/r1² = 25/16

    r2 /r1 = 5/4

    (r2 – r1)/r1 = (5 – 4)/4 * 100 = 25%

     

  • Question 7/20
    1 / -0

    The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the volume of the cylinder?(in m³)

    Solutions

    Explanation :

    r + h = 19 m

    2πr(r + h) = 1672

    r = 1672 * 7/ 2 * 22 * 19 = 14

    r = 14 ; h = 5

    volume of the cylinder = πr²h = (22/7) * 14 * 14 * 5 = 3080 m³

     

  • Question 8/20
    1 / -0

    If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m². What is the area of original rectangle?

    Solutions

    Explanation :

    length of rectangle = l m

    breadth of rectangle = b m

    l * (120/100) * b * (80/100) = 192

    1.2l * 0.8b = 192

    lb = 192 / 1.2 * 0.8 = 200 m²

     

  • Question 9/20
    1 / -0

    The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is 1232cm², What is the height?

    Solutions

    Explanation :

    4x = curved surface area = 1232

    x = 308

    5x = total surface area = 1540

    curved surface area = 2πrh

    total surface area = 2πr(r + h)

    2πr(r + h) = 1540

    2πr² + 2πrh = 1540

    2πr² = 1540 – 1232

    r = 7; h = 28

     

  • Question 10/20
    1 / -0

    The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?

    Solutions

    Explanation :

    Perimeter of square = 2 x Perimeter of rectangle

    = 2 * 2 (8+7) = 60 cm.

    Side of square = 60/4 = 15 cm = Diameter of semi-circle

    Circumference of semi-circle = πd/2 + d\

    = (22/7) * 2 * 15 + 15 = 38.57 cm

     

  • Question 11/20
    1 / -0

    If the area of a square is equal to the area of that rectangle whose width is double of the one side of the square then the ratio of the length to the breadth of the rectangle will be?

    Solutions

    Explanation :

    b = 2a

    a = b/2

    Area of square = b²/4 = Area of rectangle

    l * b = b²/4 => l = b/4

    l / b =(b/4)/b => 1:4

     

  • Question 12/20
    1 / -0

    In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 3m their ratio becomes 10:7. The area of the original rectangle in m² is?

    Solutions

    Explanation :

    [3x + 3 / 2x + 3] = 10/ 7

    x = 9

    Area of the original rectangle = 3x * 2x = 6x²

    Area of the original rectangle = 6 * 81 = 486m²

     

  • Question 13/20
    1 / -0

    The perimeter of a rectangular field is 120 m and the difference between its two adjacent sides is 30 m. The sides of the square field whose area is equal to this rectangular field is?

    Solutions

    Explanation :

    Perimeter of rectangle = 2(l + b) = 120

    l + b = 60m — (1)

    l – b = 30m –(2)

    From (1) and (2)

    l = 45 m; b = 15m

    Area of rectangle = 675m² = Area of Square

    Side of a square = 15√3

     

  • Question 14/20
    1 / -0

    If each side pair of opposite sides of a square is increased by 10m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?

    Solutions

    Explanation :

    (x+10) / x = 5 / 3

    3x + 30 = 5x

    x = 15m; Area = 225m²

     

  • Question 15/20
    1 / -0

    The area of the garden formed by two concentric circles with circumferences 44m and 176 m respectively is?

    Solutions

    Explanation :

    2πR1 = 176

    R1 = 28m

    2πR2 = 44

    R2 = 7m

    Area  of the garden = π(R1² – R2²) = 22/7(784 – 49) =2310m²

     

  • Question 16/20
    1 / -0

    One of the adjacent sides of a rectangular courtyard is 5m and its diagonal measures 13 m long. What is the area of the courtyard?

    Solutions

    Explanation :

    Another side = √[(13)² – (5)²] = 12m

    Area = 12 * 5 = 60m²

     

  • Question 17/20
    1 / -0

    The length of a park is four times of its breadth. A playground whose area is 1600 m² covers 1/4th part of the park. The length of the park is?

    Solutions

    Explanation :

    l = 4b

    Area of the park  = 4 * 1600 = 6400m²

    l * b = 6400

    l * l/4 = 6400

    l² = 6400 * 4; l = 80 * 2 = 160 m

     

  • Question 18/20
    1 / -0

    Two roads each 10m wide has been made running perpendicularly to each other inside a rectangular field of dimension 90m X 50m. What is the cost of spreading pebbles over them at the rate of Rs.8 per m².?

    Solutions

    Explanation :

    Area of Roads = (l + b – w) * w

    Area of Roads = (90 + 50 – 10) * 10 = 1300m²

    Cost = 1300 * 8 = 10400

     

  • Question 19/20
    1 / -0

    The width of a rectangular piece of land is 1/3 rd of its length. If the perimeter of the piece of land is 320m its length is?

    Solutions

    Explanation :

    length = l ; breadth = l/3

    2(l + b) = 320

    2(l + l/3) = 320

    l = 320 * 3/8 = 120m

     

  • Question 20/20
    1 / -0

    The perimeter of a square and a rectangle are equal. If the length of rectangle is 24m and breadth of the rectangle is 1/3 rd of its length, then the area of the square will be?

    Solutions

    Explanation :

    Perimeter of square = Perimeter of rectangle

    4a = 2(24 + 8)

    a = 16

    Area = 256m²

     

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