#### Data Interpretation

• ( 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 m2
• 2) 6.8 m2
• 3) 7.5 m2
• 4) 4.4 m2
• Discussion in forum
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 m2

discussion

• ( 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
• Discussion in forum
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)πr2h
= (1/3)*(22/7)*(1.75)2*12 m3
= 38.5 m3 = 38.5*100 l
= 38.5 kl.

discussion

• ( 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 m3.

• 1) 4320
• 2) 5478
• 3) 6584
• 4) 5466
• Discussion in forum
Solution : l = 8 m,
b = 6 m,
h = 3m
Volume of the cuboidal pit = l * b * h = 8 * 6 * 3 m3 = 144 m3
Cost of digging the cuboidal pit @ Rs. 30 per m3 = Rs. 144*30 = Rs. 4320.

discussion

• ( 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
• Discussion in forum
Height of the conical flask = h
Height of water in the cylindrical flask = volume of conical flask/πR2
= [(1/3)*π*r2*h]/πR2
= (1/3)*r2*h/(2r)2
= (1/3)*r2*h/4r2
= h/3*4
= h/12

discussion

• ( 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 cm3?

• 1) 60πcm2
• 2) 10πcm2
• 3) 160πcm2
• 4) 120πcm2
• Discussion in forum
Solution : Let, radius ( r ) = 3x
height ( h) = 4x
Volume of cone = 96π cm3
(1/3)πr2h = 96π
(1/3)π(3x)24x = 96π
x3 = 8
x = 2
r = 3x =3*2 = 6
h = 4x = 4*2 = 8
surface area = πr√ (r2 + h2)
= π 6√ (62 + 82)
= π 6√ (36 + 64)
=π 6√ 100
=π 6*10
= 60π cm2

discussion

• ( 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/cm3 , then the weight of the pipe is

• 1) 3.6 kg
• 2) 3.696 kg
• 3) 36 kg
• 4) 36.9 kg
• Discussion in forum
Solution : External radius = 4 cm,
Volume of iron = [(22/7) * (42 - 32) * 21]cm3 = 462 cm3
Weight of iron = (462 * 8)gm = 3696 gm = 3.696 kg

discussion

• ( 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
• Discussion in forum
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*hm3
= (2000*40*3)m3
Therefore , the volume of water flowing into the sea in one minute = (2000 * 40 * 3/60)m3
= 4000m3

discussion

• ( 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
• Discussion in forum
Answer : 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
• Discussion in forum
Answer : 4) 243 sq cm
Solution : Volume (new cube) = (13 + 63 + 83 ) = 729 cm3
a3 = 729
=> a = 7291/3
∴ Surface area of the new cube = 6a2
= 6 * 92 = 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
• Discussion in forum
Solution : Let the length of the wire be h
Radius = 1/2 mm = 1/20
πr2h = 66
(22/7)*(1/20)*(1/20)*h = 66
h = 66*20*20*7/22
= 8400 cm
= 84 m

discussion