- 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 ?
23450260262235121485NoneOption 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.
- 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
180hrs135hrs200 hrs160hrsNoneOption 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.
- 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 ?
Rs965Rs1100Rs890Rs1232NoneOption 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.
- 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.
32cm44cm36cm49cmNoneOption 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.
- 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.
2:14:53:41:2NoneOption C
Solution:
V1/V2=r12h/ r22h
=9*4/(16*3)
=3/4.
- 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:
1520120013201300NoneOption B
Solution:
2(15+12)*h=2(15*12)
54h =180*2
h=360/54=20/3
Volume= 15*12*20/3=1200cubic meter.
- The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3 . Find its height.
6m9m10m8mNoneOption 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.
- 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.
Rs965Rs1225Rs1100Rs1350NoneOption 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.
- Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm2. The circumference of each plate is:
63cm44cm52cm36cmNoneOption 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.
- 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 m3720 m3960 m3760 m3NoneOption 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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