Aptitude Questions: Mensuration Set 14

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Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for IBPS, SBI, RBI, SSC, LIC and other competitive exams. We have included some questions that are repeatedly asked in exams !!

1. A room has floor size of 15*6sq cm. What is the height of the room , if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls ?
   1.1.12cm
   2.3.24cm
   3.4.29cm
   4.2.5cm
   5.None of these
   
   Answer & Explanation

   Answer – 3.4.29cm
   Explanation :
   lb+lb = lh+hb+lh+hb
   2lb = 2h(l+b)
   h = lb/l+b
   h=15*6/15+6 = 4.29 cm
   
   
   
2. What is the volume of a right cone whose cross section is isosceles triangle with a base 10cm and slant height 13cm ?
   1.312.4 Sq cm
   2.314.2 Sq cm
   3.224.2 Sq cm
   4.354.2 Sq cm
   5.None of these
   
   Answer & Explanation

   Answer – 2.314.2 Sq cm
   Explanation :
   Base of the cone(r) =10/2 = 5 cm
   Height of the cone (h)= √169-25 =√144 = 12
   Volume = 1/3πr²h
   = 22*5*5*12/7*3 = 314.2 Sq cm
   
   
   
3. Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?
   1.10cm
   2.9cm
   3.12cm
   4.15cm
   5.None of these
   
   Answer & Explanation

   Answer – 4.15cm
   Explanation :
   Side of 1^st square = 60/4 = 15 cm.
   Smallest side of right angled triangle= 15 −6 = 9 cm.
   Length of 2^nd rectangle = 80/5 = 16 cm.
   Second largest side of the 1strectangle = 16−4 = 12 cm.
   Largest side = hypotenuse=√9^2+12^2=15cm
   
   
   
4. Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?
   1.167.3 sq cm
   2.125.8 sq cm
   3.118.9 sq cm
   4.181.2 sq cm
   5.None of these
   
   Answer & Explanation

   Answer – 3.118.9 sq cm
   Explanation :
   The side of the square = a=√961=31 cm.
   Perimeter = 4 X 31 = 124 cm
   The circumference of the circle = 5/4 x 124 = 22/7 x 2 x r
   Radius  = 155*7/44 = 24.6 cm
   Half the radius of Circle-A = 12.3 cm.
   Radius of Circle-B = 14/2 = 6.15 cm
   The area = 22/7 x 6.15 x 6.15 = 54 cm²
   
   
   
5. A horse is tethered to a peg with a 16 cm long rope at the corner of a 31 cm long and 27cm wide rectangular grass field. What area of the field will the horse graze?
   1.201.1 cm²
   2.251.6 cm²
   3.111.2 cm²
   4.245.3 cm²
   5.None of these
   
   Answer & Explanation

   Answer – 1.201.1 cm²
   Explanation :
   Area = [22*16*16/7] / 4
   = 5632/7*4 = 201.1 cm²
   
   
   
6. The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?
   1.35.8 m²
   2.36.5 m²
   3.30.5 m²
   4.38.5 m²
   5.None of these
   
   Answer & Explanation

   Answer – 4.38.5 m²
   Explanation :
   Radius = Breadth /2 = 7/2 = 3.5
   Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m²
   
   
   
7. In a swimming pool measuring 80 cm x 30 cm, 120 men take a dip. If the average displacement of water by a man is 5 cm cube, What will be the rise in water level  ?
   1.1/5 cm
   2.1/3 cm
   3.1/2 cm
   4.1/4 cm
   5.None of these
   
   Answer & Explanation

   Answer – 4.1/4 cm
   Explanation :
   Total volume displaced by 8 men= 120×5 cm cube
   However volume=lxbxh=80x30xh
   80x30xh=120×5
   h=120*5/80*30 = 600/2400 = 0.25.
   so the water level rises by 0.25 cm = ¼ cm
   
   
   
8. A cylindrical tank of diameter 14 cm is full of water. If 9 litres of water is drawn off, the water level in the tank will drop by
   1.230.6 cm
   2.223.5 cm
   3.233.8 cm
   4.238.3 cm
   5.None of these
   
   Answer & Explanation

   Answer – 3.233.8 cm
   Explanation :
   1 litres =  1000 cm
   9 litres = 9000 cm
   Volume of cylinder = πr²h
   22/7*7*7*h = 11000
   h = 9000*7*4/22*7*7 = 233.8 cm
   
   
   
9. A circular wire of diameter 42cm is folded in the shape of a rectangle whose sides are in the ratio 6:5. Find the ratio of the enclosed rectangle ?
   1.1080cm²
   2.1181cm²
   3.1250cm²
   4.1800cm²
   5.None of these
   
   Answer & Explanation

   Answer – 1.1080cm²
   Explanation :
   Radius = 42/2 = 21cm
   Circumference = 2*22*21/7 = 132cm
   L:b = 6x:5x
   Perimeter of the rectangle = 2(6x+5x) = 22x
   22x = 132
   X = 6
   Area = 6x * 5x = 30x*x
   =30*6*6 = 1080cm²
   
   
   
10. A cylindrical tub of radius 10 cm contains water up to a depth of 25cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 5cm. What is the radius of the iron ball(approximate) ?
    1.19
    2.15
    3.14
    4.17
    5.None of these
    
    Answer & Explanation

    Answer – 3.14
    Explanation :
    Volume of the ball = volume of the raised water
    4*22*r³/3*7 = 22*100*5
    r³ = 11000*3*7/88 = 2625
    r = 13.79 or 14