Aptitude Questions – Mensuration Set 18

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1. A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?
   A. 10 cm
   B. 18 cm
   C. 12 cm
   D. 16 cm
   E. None of these
   
   Answer & Explanation

   Answer – B. 18 cm
   Explanation :
   Volume of the Rectangular Block = 22 * 18 * 7
   Radius of the Cistern = 7 cm
   Area of the Cylinder = Π * r² * h = 22/7 * 7 * 7 * h
   22/7 * 7 * 7 * h = 22 * 18 * 7; h = 18 cm
   
   
2. If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?
   A. 100%
   B. 150%
   C. 125%
   D. 175%
   5. None of these
   
   Answer & Explanation

   Answer – A. 100%
   Explanation :
   R1/R2 = R/2R & H1/H2 = H/H/2
   Original Volume = πr²h
   New Volume = π(2r)²h/2
   Change in Volume = (2 – 1)/1 * 100 = 100
   
   
3. The perimeter of a rectangle and a square is 80 cm each. If the difference between their areas is 100 cm. Find the sides of the rectangle.
   A. 30cm, 10cm
   B. 40cm, 15cm
   C. 25cm, 10cm
   D. 20cm, 30cm
   E. None of the Above
   
   Answer & Explanation

   Answer – A. 30cm, 10cm
   Explanation :
   2(l + b) = 4a = 80
   l + b = 40; a = 20 => a² = 400
   a² – lb = 100; 400 – lb =100; lb = 300
   (l – b)² = (l + b)² – 4lb
   (l – b)² = 1600 – 1200; l – b = 20;
   
   
4. The length of a wall is 5/4 times of its height. If the area of wall will be 500m². What is the sum of the length and height of the wall?
   A. 55m
   B. 45m
   C. 40m
   D. 50m
   E. None of these
   
   Answer & Explanation

   Answer – B. 45m
   Explanation :
   l = 5x; h = 4x ; l * h = 500
   20x² = 500 ; x = 5
   l + h = 25 + 20 = 45m
   
   
5. A circular path runs round a circular garden. If the difference between the circumference of the outer circle and inner circle is 88m. Find the width of Path?
   A. 14 m
   B. 15 m
   C. 18 m
   D. 13 m
   E. None of the Above
   
   Answer & Explanation

   Answer – A. 14 m
   Explanation :
   Width of the Road = R – r
   2πR – 2πr = 88
   R – r = 14 m
   
   
6. The radius of a circle is 4 m. What is the radius of another circle whose area is 16 times of that first?
   A. 16 m
   B. 64 m
   C. 256 m
   D. 400 m
   E. None of these
   
   Answer & Explanation

   Answer – A. 16 m
   Explanation :
   Ratio of areas = (ratio of radii)²
   16/1 = (ratio of radii)²
   ratio of radii = 4/1
   The required radius = 16 m
   
   
7. What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?
   A. 27m
   B. 28m
   C. 29m
   D. 25m
   E. 15m
   
   Answer & Explanation

   Answer – C. 29m
   Explanation :
   πR² = πr1² + πr2²
   πR² = π(r1² + r2²)
   R² = (400 + 441)
   R = 29
   
   
8. Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.
   A. 3080 cm²
   B. 2300 cm²
   C. 3460 cm²
   D. 3600 cm²
   E. None of these
   
   Answer & Explanation

   Answer – A. 3080 cm²
   Explanation :
   r = 20 ; h = 21
   l = √(400 + 441) = 29 cm
   Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²
   
   
9. A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter be 54 cm and the length of the tube be 490 cm, find the volume of plastic.
   A. 320000 cm³
   B. 340000 cm³
   C. 306300 cm³
   D. 308000 cm³
   E. None of these
   
   Answer & Explanation

   Answer – B. 640640 cm³
   Explanation :
   Explanation :
   External Radius = 27; Internal Radius = 23
   Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³
   
   
10. A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?
    A. 53500
    B. 49500
    C. 51500
    D. 52500
    E. None of these
    
    Answer & Explanation

    Answer – D. 52500
    Explanation :
    Explanation :
    Number of cones =Volume of Cylinder / Volume of one cone
    = π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)
    = 52500