Quantitative Aptitude: Mensuration Questions Set 4

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

1. The height of the cone is 24 cm and the curved surface area of cone is 550 cm². Find its volume.
   A) 1200 cm²
   B) 1232 cm²
   C) 1240 cm²
   D) 1260 cm²
   E) 1262 cm²
   
   View Answer

   Option B
   Solution:
   Volume= 1/3 π*r² * h
   Answer will be divisible by 11, as in pie we have 2*11. As only 1232 is divisible by 11, it is the answer
2. The side of a square base of a pyramid increases by 20% and its slant height increases by 10%. Find the per cent change in Curved Surface Area.
   A) 28%
   B) 58.4%
   C) 32%
   D) 45.20%
   E) 48%
   
   View Answer

   Option C
   Solution:
   C.S.A=1/2*(perimeter of base)*l
   20+10+(20*10)/100=32%
   
3. If a copper wire is bend to make a square whose area is 324 cm². If the same wire is bent to form a semicircle, then find the radius of semicircle.
   A) 7 cm
   B) 14 cm
   C) 11 cm
   D) 21 cm
   E) 12 cm
   
   View Answer

   Option B
   Solution:
   Area of square= 324, hence side =18
   Perimeter = 4a =4*18=72
   Circumference of semicircle= 2r+Pie *r
   r(2+pie)=72
   r=14 cm
4. A man wants to make small sphere of size 1 cm of radius from a large sphere of size of 6 cm of radius. Find out how many such sphere can be made?
   A) 216
   B) 125
   C) 36
   D) 200
   E) 64
   
   View Answer

   Option A
   Solution:
   Volume of sphere1/volume of sphere 2= required number of sphere
   =6*6*6/1*1*1=216
5. A sphere of radius 9 cm is dip into a cylinder who is filled with water upto 20 cm. If the radius of cylinder is 6 cm find the percentage change in height.
   A) 50%
   B) 40%
   C) 55%
   D) 45%
   E) 57%
   
   View Answer

   Option D
   Solution:
   Volume of sphere= volume of cylinder from height 20 cm to upwards.
   4/3 * π * 9*9*9 = π * 6*6*h
   h=9
   new height=20+9=29
   %change= 9/20*100=45%
   
6. The length of the perpendicular drawn from any point in the interior of an equilateral triangle to the respective sides are P1, P2 and P3. Find the length of each side of the triangle.
   A) 2/√3 *(P1 + P2 + P3)
   B) 1/3 * (P1 + P2 + P3)
   C) 1/√3 *(P1 + P2 + P3)
   D) 4/√3 *(P1 + P2 + P3)
   E) 5/√3 *(P1 + P2 + P3)
   
   View Answer

   Option A
7. A conical cup is filled with ice cream. The ice cream forms a hemispherical shape on its top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of cone then the volume of ice cream is?
   A) 1078 cm³
   B) 1708 cm³
   C) 7108 cm³
   D) 7180 cm³
   E) 1808 cm³
   
   View Answer

   Option A
   Solution:
   Volume = volume of hemisphere + volume of cone= 2/3* π *r³ + 1/3 π * r² *h
   =1078
8. Assume that a drop of water is spherical and its diameter is one tenth of a cm. A conical glass has equal height to its diameter of rim. If 2048000 drops of water fill the glass completely then find the height of the glass.
   A) 12 cm
   B) 16 cm
   C) 20 cm
   D) 8 cm
   E) 10 cm
   
   View Answer

   Option B
   Solution:
   diameter of drop of water=1/10 => radius=1/20
   volume of 204800 drop of water=204800*4/3* π*1/20 *1/20*1/20 = 1024 π/3
   Volume of cone=1024 π/3 = 1/3 * π *r² * h (r=h/2)
   h=16
   
9. If the radius of a sphere increase by 4 cm then the surface area increase by 704 cm² . The radius of the sphere initially was?
   A) 5
   B) 4
   C) 6
   D) 8
   E) 10
   
   View Answer

   Option A
   Solution:
   4 π(r+4)² – 4 * π*r² = 704
   solve and get r=5
10. By melting two solid metallic spheres of radii 1 cm and 6 cm, a hollow sphere of thickness 1 cm is made. The external radius of the hollow sphere will be.
    A) 8 cm
    B) 9 cm
    C) 6 cm
    D) 7 cm
    E) 10 cm
    
    View Answer

    Option B
    Solution:
    4/3* π (R³ + r³)= 4/3* π * ((x+1)³ – x³)
    R=6 cm; r=1 cm; x= radius of hollow sphere inner; (x+1)=outer radius
    solve and get x=8
    outer=x+1=9 cm