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
    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
    C.S.A=1/2*(perimeter of base)*l
  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
    Area of square= 324, hence side =18
    Perimeter = 4a =4*18=72
    Circumference of semicircle= 2r+Pie *r
    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
    Volume of sphere1/volume of sphere 2= required number of sphere
  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
    Volume of sphere= volume of cylinder from height 20 cm to upwards.
    4/3 * π * 9*9*9 = π * 6*6*h
    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
    Volume = volume of hemisphere + volume of cone= 2/3* π *r3 + 1/3 π * r2 *h
  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
    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)
  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
    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
    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

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