# 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.