Quantitative Aptitude: Mensuration Questions Set 8

  1. The cost of fencing around a circular field is Rs 8580 at the rate of Rs 15 per foot . What is the area of the circular field ?
    23450
    26026
    22351
    21485
    None
    Option B
    Solution:
    Fencing = 8580/15=572= Circumference of a circle field
    2πr = 572
    2*22/7*r = 572
    r=91
    Area = 22/7 *91 * 91 = 26026 sq meter.
  2. Water flows into a tank which is 200m long and 150m wide, through a pipe of cross-section 0.3m * 0.2m at 20 km/hour. Then the time (in hours) for the water level in the tank to reach 8m is
    180hrs
    135hrs
    200 hrs
    160hrs
    None
    Option C
    Solution:
    speed of water = 20 km/hour
    = 20000 m/hour
    Area of base = 0.3m × 0.2m
    = 0.06 sq. meter
    Volume of water flows in 1 hour = area of base× speed of water in 1 hour
    = 0.06 × 20000
    = 1200 cubic meter
    Volume of tank up to 8 m height = 200 × 150 ×
    = 240000 cubic meter
    Time to reach the water 8 m high = 240000/1200
    = 200 hrs.
  3. The outer circumference of a circular track is 220 m. The track is 14 m wide everywhere. Calculate the cost of levelling the track at the rate of 50 paisa/square meter ?
    Rs965
    Rs1100
    Rs890
    Rs1232
    None
    Option D
    Solution:
    Let outer radius = R
    Inner radius = r = R – 14
    2 * 22/7 *r = 220
    R = 220/(2*22) * 7 = 35m
    r = 35 – 14 = 21 m.
    Area of track = 22/7 (R2 – r2 )
    = 22/7{352 –212 } = 2464 m2
    Cost of levelling the track = 2464×0.50 = Rs. 1232.
  4. A cone and sphere have the same radius of 12 cm. Find the height of the cone if the cone and sphere have the same volume.
    32cm
    44cm
    36cm
    49cm
    None
    Option E
    Solution:
    Volume of the cone=1/3πr2h
    =1/3*π*122*h==>48 πh
    Volume of the sphere=4/3 π r3
    =4/3* π*123==>2304 π
    Both are equal then
    2304 π=48 πh
    h= 2304/48=48cm.
  5. Two cones have their heights in the ratio 4:3 and the radii of their bases in the ratio 3:4. Find the ratio of their volumes.
    2:1
    4:5
    3:4
    1:2
    None
    Option C
    Solution:
    V1/V2=r12h/ r22h
    =9*4/(16*3)
    =3/4.
  6. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
    1520
    1200
    1320
    1300
    None
    Option B
    Solution:
    2(15+12)*h=2(15*12)
    54h =180*2
    h=360/54=20/3
    Volume= 15*12*20/3=1200cubic meter.
  7. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3 . Find its height.
    6m
    9m
    10m
    8m
    None
    Option A
    Solution:
    Volume/curved surface area=πr2 h/2πrh==> r/2=924/264*2=7m.
    Then Area 264=2*22/7*7*h
    h= 6m.
  8. The cost of the paint is Rs.24.50 per kg. If 1kg of paint covers 12sq.ft, how much will it cost to paint outside of a cube having 10 feet each side.
    Rs965
    Rs1225
    Rs1100
    Rs1350
    None
    Option B
    Solution:
    Surface area of a cube= 6 * (10 * 10) = 600 sq.ft
    Quantity of paint required=(600/12)=50kg
    Cost of painting= 24.5*50 = Rs.1225.
  9. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm2. The circumference of each plate is:
    63cm
    44cm
    52cm
    36cm
    None
    Option B
    Solution:
    Side of square paper=√784=28cm
    Radius of each circular plate=1/4*28=7cm.
    Circuference of each circular plate=2*22/7*7=44cm.
  10. A metallic sheet is of rectangular shape with dimensions 32 m x 18 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 4 m, the volume of the box (in m3) is:
    840 m3
    720 m3
    960 m3
    760 m3
    None
    Option C
    Solution:
    l = (32 – 8)m = 24 m,
    b = (18 -8)m = 10 m,
    h = 4 m.
    Then Volume of the box = (24 *10 * 4) m3= 960 m3.



 

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