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( 1 ) In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
 1) 5.6 m^{2}
 2) 6.8 m^{2}
 3) 7.5 m^{2}
 4) 4.4 m^{2}

Show Answer Report Discussion in forumAnswer : 4) 4.4 m^{2}
Solution : Given,
h = 28 m
2r = 5 cm
r = 5/2 cm = 5/(2*100) m = 5/200 m 1/40 m
Total radiating surface in the system = 2πrh
= 2*(22/7)*(1/40)*28 = 4.4 m^{2}
discussion
Answer : 4) 4.4 m^{2}



( 2 ) A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
 1) 37.6 kl
 2) 38.5 kl
 3) 39.5 kl
 4) 44.2 kl

Show Answer Report Discussion in forumAnswer : 2) 38.5 kl
Solution : Given,
diameter = 3.5 cm
Radius ( r ) = 3.5/2 m = 1.75 m
Depth (h) = 12 m
capacity of the conical pit = (1/3)πr^{2}h
= (1/3)*(22/7)*(1.75)^{2}*12 m^{3}
= 38.5 m^{3} = 38.5*100 l
= 38.5 kl.
discussion
Answer : 2) 38.5 kl



( 3 ) Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs.30 per m^{3}.
 1) 4320
 2) 5478
 3) 6584
 4) 5466

Show Answer Report Discussion in forumAnswer : 1) 4320
Solution : l = 8 m,
b = 6 m,
h = 3m
Volume of the cuboidal pit = l * b * h = 8 * 6 * 3 m^{3} = 144 m^{3}
Cost of digging the cuboidal pit @ Rs. 30 per m^{3} = Rs. 144*30 = Rs. 4320.
discussion
Answer : 1) 4320



( 4 ) A conical flask of base radius 'r' and height 'h' is full of water. The water is now poured into a cylinderical flask of radius '2r'. What is the height to which water will rise in the flask?
 1) h/2
 2) h/6
 3) h
 4) h/12

Show Answer Report Discussion in forumAnswer : 4) h/12
Solution : Radius of the conical flask = r
Height of the conical flask = h
Radius of the cylindrical flask ( R ) = 2r
Height of water in the cylindrical flask = volume of conical flask/πR^{2}
= [(1/3)*π*r^{2}*h]/πR^{2}
= (1/3)*r^{2}*h/(2r)^{2}
= (1/3)*r^{2}*h/4r^{2}
= h/3*4
= h/12
discussion
Answer : 4) h/12



( 5 ) Find the lateral surface area , if the radius and height of a right circular cone are in the ratio 3:4 and its volume is 96π cm^{3}?
 1) 60πcm^{2}
 2) 10πcm^{2}
 3) 160πcm^{2}
 4) 120πcm^{2}

Show Answer Report Discussion in forumAnswer : 1) 60πcm^{2}
Solution : Let, radius ( r ) = 3x
height ( h) = 4x
Volume of cone = 96π cm^{3}
(1/3)πr^{2}h = 96π
(1/3)π(3x)^{2}4x = 96π
x^{3} = 8
x = 2
r = 3x =3*2 = 6
h = 4x = 4*2 = 8
surface area = πr√ (r^{2} + h^{2})
= π 6√ (6^{2} + 8^{2})
= π 6√ (36 + 64)
=π 6√ 100
=π 6*10
= 60π cm^{2}
discussion
Answer : 1) 60πcm^{2}



( 6 ) A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weigh 8 g/cm^{3} , then the weight of the pipe is
 1) 3.6 kg
 2) 3.696 kg
 3) 36 kg
 4) 36.9 kg

Show Answer Report Discussion in forumAnswer : 2) 3.696 kg
Solution : External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron = [(22/7) * (42  32) * 21]cm^{3} = 462 cm^{3}
Weight of iron = (462 * 8)gm = 3696 gm = 3.696 kg
discussion
Answer : 2) 3.696 kg



( 7 ) A river 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into sea in a minute?
 1) 4000000
 2) 4000
 3) 40000
 4) 400000

Show Answer Report Discussion in forumAnswer : 2) 4000
Solution : Since the water flows at the rate of 2 km per hour, the water from 2 km of river flows into the sea in one hour.
Therefore The volume of water flowing into the sea in one hour = Volume of the cuboid
= l*b*hm^{3}
= (2000*40*3)m^{3}
Therefore , the volume of water flowing into the sea in one minute = (2000 * 40 * 3/60)m^{3}
= 4000m^{3}
discussion
Answer : 2) 4000



( 8 ) If the side of a cube is increased by x%, then find increase in percent of its volume .
 1) [(1 + x/100)^{3} 1] *100 %
 2) [(1 + x/100)^{3}  1]%
 3) [(1 + 2x/100)^{3}  1]
 4) None of these

Show Answer Report Discussion in forumAnswer : 1) [(1 + x/100)^{3} 1] *100 %
Solution : According to the formula,
Percentage increase in volume = [(1 + x/100)^{3}  1] * 100%
discussion
Answer : 1) [(1 + x/100)^{3} 1] *100 %



( 9 ) Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half the surface area of the new cube?
 1) 153 sq cm
 2) 135 sq cm
 3) 235 sq cm
 4) 243 sq cm

Show Answer Report Discussion in forumAnswer : 4) 243 sq cm
Solution : Volume (new cube) = (1^{3} + 6^{3} + 8^{3} ) = 729 cm^{3}
a^{3} = 729
=> a = 729^{1/3}
∴ Surface area of the new cube = 6a^{2}
= 6 * 9^{2} = 486 sq cm
Surface area/2 = 486/2 = 243 sq cm
discussion
Answer : 4) 243 sq cm



( 10 ) 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
 1) 84
 2) 90
 3) 168
 4) 336

Show Answer Report Discussion in forumAnswer : 1) 84
Solution : Let the length of the wire be h
Radius = 1/2 mm = 1/20
πr^{2}h = 66
(22/7)*(1/20)*(1/20)*h = 66
h = 66*20*20*7/22
= 8400 cm
= 84 m
discussion
Answer : 1) 84
