Aptitude Questions: Mensuration Set 11

Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

1. 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)?
   A. 16.25
   B. 19.25
   C. 18.25
   D. 17.25
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 19.25
   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
   
   
2. 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?
   A. 160
   B. 450
   C. 250
   D. 325
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 450
   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
   
   
3. 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)?
   A. 154
   B. 452
   C. 616
   D. 512
   E. None of the Above
   
   Answer & Explanation

   Answer – C. 616
   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
   
   
4. 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).
   A. 160 metre
   B. 80 metre
   C. 82 metre
   D. 84 metre
   E. None of the Above
   
   Answer & Explanation

   Answer – D. 84 metre
   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
   
   
5. 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.
   A. 15m, 9m
   B. 17m, 9m
   C. 14m, 7m
   D. 16m, 7m
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 17m, 9m
   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
   
   
6. 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?
   A. 25%
   B. 35%
   C. 45%
   D. 50%
   E. None of the Above
   
   Answer & Explanation

   Answer – A. 25%
   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%
   
   
7. 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)
   A. 3080
   B. 2940
   C. 3220
   D. 2660
   E. 2800
   
   Answer & Explanation

   Answer – A. 3080
   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
   
   
8. 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?
   A. 100m²
   B. 150m²
   C. 175m²
   D. 200m²
   E. None of the Above
   
   Answer & Explanation

   Answer – D. 200m²
   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
   
   
9. 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?
   A. 14 cm
   B. 28 cm
   C. 7 cm
   D. 56 cm
   E. 24 cm
   
   Answer & Explanation

   Answer – B. 28 cm
   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
   
   
10. 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 ?
    A. 38.57 cm
    B. 23.57 cm
    C. 42.46 cm
    D. 47.47 cm
    E. None of the Above
    
    Answer & Explanation

    Answer – A. 38.57 cm
    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