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6.
The Radius at the base of a conical tent is 7 metres. If the slant height of the tent is 15 metres, what is the area of the canvas required to make the tent?
  • A.
    330 sq.cm
  • C.
    300 sq.cm
  • B.
    30 sq.cm
  • D.
    60 sq.cm
  • Answer & Explanation
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Answer : [A]
Explanation :
  r = 7 metres

l = 15 metres
Area of canvas required = C.S.A of cone
  = rl =
22
7
 x 7 x 15 = 330 sq.m  
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7.
The diagonal of a cube  is 2 3  metres. Its volume in cubic centimeter will be    
  • A.
    0.000008
  • C.
    8000000
  • B.
    8
  • D.
    80000
  • Answer & Explanation
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Answer : [C]
Explanation :
Volume of the cube =
1
3 3
 (diagonal)3    
=
1
3 3
  (2 3  x 102)3 =
3 x 8
3
 x 106 = 8 x 106 cm3 = 8000000  
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8.
A hemisphere of radius 6 cm is case into a right circular cone of height 75 cm. What is the radius of the base of cone?
  • A.
    3 cm
  • C.
    2.6 cm
  • B.
    2.4 cm
  • D.
    1.4 cm
  • Answer & Explanation
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Answer : [B]
Explanation :
Let r1 be the radius of the hemisphere and r2 be the radius of the cone.
Volume of hemisphere = Volume of cone
2
3
r13
=
1
3
r22h
 
2
3
(6)3
=
1
3
r22 x 75
 
r22 =
3
75
x
2
3
 x (6)3  
=
2
25 x 3
 x 6 x 6 x 6
 
r22 =
6 x 6 x 4
25
 
r2 =
6 x 2
5
 
 r2 =
12
5
 = 2.4 cm
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9.
Find the slant height of the cone whose height is 4.8 cm and the diameter of base is 4 cm.
  • A.
    6.2 cm
  • C.
    5.2 cm
  • B.
    7.2 cm
  • D.
    4.2 cm
  • Answer & Explanation
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Answer : [C]
Explanation :
h = 4.8 cm, r = 2 cm
l = h2 + r2 = (4.8)2 + 22 = 23.04 + 4 = 27.04  = 5.2 cm
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10.
2.2 cu. Cm of brass is to be drawn into cylindrical wire. ¼ cm in diameter. What will be the length of the wire?
  • A.
    448 m
  • C.
    400 m
  • B.
    420 m
  • D.
    432 m
  • Answer & Explanation
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Answer : [A]
Explanation :
Let the length of the wire be = l cm
Diameter of wire =
1
4
 cm
 
  Radius =
1
8
 cm
Volume of wire =
x
1
8
x
1
8
 x l cu.cm  
But, volume = 2.2 cu.cm = 2200 cu.dm (  1 cu.dm = 1000 cu.cm)
22
7
x
1
64
 x l = 2200
 
l = 2200 x
7
22
 x 64  
  = 700 x 64 = 44800 cm = 448 m  
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