Quantitative Aptitude: Mensuration Questions Set 3

Mensuration Questions SBI PO, NIACL, IBPS PO, NICl, LIC, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams

1. A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edge of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volumes of cube is 216 cm³ , what is the volume of the cone (approximately)?
   A) 56 cm³
   B) 60 cm³
   C) 46 cm³
   D) 50 cm³
   E) None of these
   
   View Answer

   Option A
   Solution:
   
   radius of cone= a/2
   volume(a³)=216 , hence a=6
   r= 3 cm; height of the cone= 6cm (as it is fitted in this cube of side 6 cm, hence its height will also be 6 cm)
   Volume of cone= 1/3 π*r² * h
   =56
   
2. The diagram shows a section of a rocket firework. If this section can be completely filled with gunpowder what is the volume of gunpowder required?
   A) 1882 cm³
   B) 1782 cm³
   C) 1982 cm³
   D) 1682 cm³
   E) None of these
   
   View Answer

   Option B
   Solution:
   
   sin 60 = P/H=r/6=√3/2
   => r=3√3 cm
   In the cone; 6² = h² + r²
   h=3 cm
   Volume of Gunpowder= Volume of Cone+ Volume of Cylinder=1/3 πr²h + πr²h = πr² (1/3 h+h)
   =22/7*27*21=1782
3. If a square, circle and rectangle has same perimeter then which one of them has the maximum area?
   A) Square
   B) Circle
   C) Rectangle
   D) All have equal area
   E) Cannot be determined
   
   View Answer

   Option B
   Solution: In such case the area in descending order is: Circle> Square> Rectangle
4. A cylinder has some water at height 20 cm. If a sphere of radius 6 cm is poured into it then find the rise in height of water if the radius of cylinder is 8 cm.
   A) 3.5 cm
   B) 9.5 cm
   C) 4.5 cm
   D) 5.5 cm
   E) None of these
   
   View Answer

   Option C
   Solution:
   
   Volume of ball= volume of rising water in the cylinder
   4/3 * π*r³ = π*r² *h
   4/3*6*6*6=8*8*h
   h=4.5 cm
   
5. If the base of a pyramid is square and its side is 4√2 cm and slant height of pyramid is 5 cm, find the volume of pyramid.
   A) 48 cm³
   B) 16 cm³
   C) 24 cm³
   D) 32 cm³
   E) None of these
   
   View Answer

   Option D Solution:
   l=slant height=5 cm ; h=height; side=4√2 cm
   l² = h² + [(side*√2)/2]²
   Note: The content inside bracket is the calculation for half of the diagonal of the square.
   h= 3 cm
   volume= 1/3 * Area of base * h
   =1/3 * 32 * 3= 32
6. A sphere of 5 cm radius is melted and small sphere of radius 1 cm is made from it. Find the number of sphere that can be made from it.
   A) 25
   B) 125
   C) 50
   D) 100
   E) None of these
   
   View Answer

   Option B
   Solution: Number of sphere=Volume of large sphere/volume of small sphere
   [4/3* π *r1³ ]/ [4/3* π *r2³ ]=5*5*5/1*1*1=125
7. A person wants to make a cylindrical box which is open from the top. If the height of that box is 10 cm and radius is 7 cm find the area of sheet which is required to make it.
   A) 880 cm²
   B) 1188 cm²
   C) 594 cm²
   D) 440 cm²
   E) None of these
   
   View Answer

   Option C
   Solution: Area required=Curved surface area + Area of base= 2 π r h + π r² = 594
8. A square park has a 2 m wide cross road in middle of it. If the side of park is 100 m then find the remaining area of the park.
   A) 9650 m²
   B) 9596 m²
   C) 9600 m²
   D) 9604 m²
   E) None of these
   
   View Answer

   Option D
   Solution:
   Total area= 10000
   road area= 2*100 + 2*100- 2*2=396
   remaining area=10000-396=9604
   
9. In a right circular cone the radius of its base is 6 cm and its height is 14 cm. A cross section is made through the mid-point of the height parallel to the base. The volume of the lower portion is?
   A) 528 cm³
   B) 366 cm³
   C) 498 cm³
   D) 462 cm³
   E) None of these
   
   View Answer

   Option D Solution:
   
   Volume of cone= 1/3 π*r² * h
   Volume of lower part=volume of full cone-volume of upper cone
   for full cone take r=6, h=14
   for upper cone take r1=r/2=3 and h=7
   volume of lower part=528-66=462
   
10. If radius of cone decrease by 50% and height increase by 20%. Then find the percentage change in the volume.A) 70% decrease
    B) 70% increase
    C) 40% decrease
    D) 40% increase
    E) 20% increase
    
    View Answer

    Option A
    Solution:
    Volume of cone= 1/3 π*r² * h
    r=50% dec =1/2 =>2————1
    2———–1(dec)
    h=20% inc =1/5 =>5————-6 (inc)
    2*2*5:1*1*6=10:3
    (3-10)/10*100=70% dec