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91. Two circular cylinders of equal curved surface areas have their radii in the ratio of 3 : 4. Find the ratio of their volumes.
  A.  3 : 4
  B.  2 : 5
  C.  5 : 3
  D.  3 : 7
     
   
View Answer

Shortcut:
If the ratio of radii of two circular cylinders of equal curved surface area are given, then the ratio of their volumes is given by the following result.
Ratio of volumes = Ratio of radii
If in plae of cylinder, cones are given, this formula is applicable.
Here, Ratio of radii = 3 : 4
Using these values in the shortcut, we get:
Ratio of volumes = 3 : 4

92. Two circular cylinders of equal curved surface areas have their heights in the ratio of 3 : 4. Find the ratio of their volumes.
  A.  4 : 5
  B.  4 : 3
  C.  3 : 5
  D.  5 : 8
     
   
View Answer

Shortcut:
If the ratio of heights of two circular cylinders of equal curved surface area are given, then the ratio of their volumes is given by the following result.
Ratio of volumes = Inverse ratio of heights
If in plae of cylinder, cones are given, this formula is applicable.
Here, Ratio of heights = 3 : 4
Using these values in the shortcut, we get:
Ratio of volumes =
1 / 3
:
1 / 4
= 4 : 3

93. Two circular cylinders of equal curved surface areas have their height in the ratio of 3 : 4. Find the ratio of their radii.
  A.  4 : 5
  B.  3 : 5
  C.  4 : 3
  D.  3 : 7
     
   
View Answer

Shortcut:
If the ratio of heights of two circular cylinders of equal curved surface areas are given, then the ratio of their radii is given by the following result.
Ratio of radii = Inverse ratio of heights
Here, Ratio of heights = 3 : 4
Using these values in the shortcut, we get:
Ratio of radii =
1 / 3
:
1 / 4
= 4 : 3

94. Two right circular cones of equal curved surface areas have their heights in the ratio of 3 : 4. Find the ratio of their radii.
  A.  4 : 5
  B.  2 : 5
  C.  4 : 3
  D.  5 : 3
     
   
View Answer

Shortcut:
If the ratio of slant heights of two right-circular cones of equal curved surface areas are given, then the ratio of their radii is given by the following result.
Ratio of radii = Inverse ratio of slant heights
Here, Ratio of heights = 3 : 4
Using these values in the shortcut, we get:
Ratio of radii =
1 / 3
:
1 / 4
= 4 : 3

95. Sides of two cubes are in the ratio 2 : 3. Find the ratio of their volumes.
  A.   8 : 27
  B.   1 : 8
  C.   9 : 64
  D.   8 : 125
     
   
View Answer

Shortcut:
If the ratio of sides of two cubes are given, then the ratio of their volumes is given by the following result.
Ratio of volumes = (Ratio of sides)3
Here, Ratio of sides = 2 : 3
Using these values in the shortcut, we get:
Ratio of volumes = (2 : 3)3 = 8 : 27

96. Sides of two cubes are in the ratio of 2 : 3. Find the ratio of their surface areas.
  A.  9 : 16
  B.  4 : 25
  C.  9 : 16
  D.  4 : 9
     
   
View Answer

Shortcut:
If the ratio of sides of two cubes are given, then the ratio of their surface areas is given by the following result.
Ratio of surface areas = (Ratio of sides)2
Here, Ratio of sides = 2 : 3
Using these values in the shortcut, we get:
Ratio of surface areas = (2 : 3)2 = 4 : 9

97. Volumes of two cubes are in the ratio of 1 : 8. Find the ratio of their surface areas.
  A.  1 : 4
  B.  1 : 3
  C.  1 : 5
  D.  1 : 9
     
   
View Answer

Shortcut:
If the ratio of volumes of two cubes are given, then the ratio of their surface areas is given by the following result.
(Ratio of surface areas)3 = (Ratio of volumes)2
Here, Ratio of volumes = 1 : 8
Using these values in the shortcut, we get:
(Ratio of surface areas)3 = (1 : 8)2
(Ratio of surface areas)3 = 1 : 64
(Ratio of surface areas) = (1 : 64)1/3
(Ratio of surface areas) = (1 : 4)3 x 1/3
Ratio of surface areas = 1 : 4

98. If the heights of two cones are in the ratio 1 : 4 and their diamerers in the ratio 4 : 5, what is the ratio of their volumes?
  A.  4 : 25
  B.  9 : 25
  C.  4 : 9
  D.  7 : 15
     
   
View Answer

Shortcut:
If the ratio of heights (not slant height) and the ratio of diameters or radii of two right circular cones ae given, then the ratio of their volumes can be given by the following result.
Ratio of volumes = (Ratio of radii)2 x (Ratio of heights)
[Note: This formula also holds good for cyinders]
[ratio of diameters = ratio of radii] Here, Ratio of heights = 1 : 4
Ratio of diameter = 4 : 5
Using these values in the shortcut, we get:
Ratio of volumes = (4 : 5)2 x (1 : 4)
Ratio of volumes = (16 : 25) x (1 : 4)
=
16 / 25
x
1 / 4
=
4 / 25
= 4 : 25

99. If the radii of two cones are in the ratio 1 : 4 and their volumes in the ratio 4 : 5, what is the ratio of their heights?
  A.  27 : 5
  B.  64 : 5
  C.  8 : 7
  D.  9 : 11
     
   
View Answer

Shortcut:
If the ratio of radii and the ratio of volumes of two right circular cones are given, then the ratio of their heights can be given by the following result.
Ratio of heights = (Inverse ratio of radii)2 x (Ratio of volumes)
[Note: This formula also holds good for cyinders]
Here, Ratio of radii = 1 : 4
Ratio of volumes = 4 : 5
Using these values in the shortcut, we get:
Ratio of heights =
(
1 / 1
:
1 / 4
)
2 x (4 : 5)
=
(
1 :
1 / 16
)
x (4 : 5)
= 16 x
4 / 5
= 64 : 5

100. If the volumes of the two cones are in the ratio 4 : 1 and their heights in the ratio 4 : 9, what is the ratio of their radii?
  A.  2 : 1
  B.  4 : 1
  C.  4 : 1
  D.  3 : 1
     
   
View Answer

Shortcut:
If the ratio of volumes of ratio of heights of two right circular cones are given, then the ratio of their radii is given by the following result.
Ratio of radii = √[(Ratio of volumes)(Inverse ratio of heights)]
Here, Ratio of heights = 4 : 9
Ratio of volumes = 4 : 1
Using these values in the shortcut, we get:
Ratio of radii =
√[
(4 : 1)
(
1 / 4
:
1 / 9
)]

= √[(4 : 1)(9 : 4)]
√(
4 / 1
x
9 / 4
)
= √(9 : 1) = 3 : 1

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