Home ≫ Arithmetic Aptitute ≫ Elementary Mensuration-II ≫ Page 9
81. The radii of two spheres are in the ratio of 1 : 2. What is the ratio of their volumes?
  A.   1 : 9
  B.   1 : 6
  C.   1 : 8
  D.   1 : 5
     
   
View Answer

Shortcut:
If the ratio of radii of the two spheres are given, then the ratio of their volumes will be obtained from the following result.
(Ratio of the radii)3 = (Ratio of volumes)
Here, Ratio of the radii = 1 : 2
Using these values in the shortcut, we get:
(1 : 2)3 = (Ratio of volumes)
1 : 8 = (Ratio of volumes)
∴ Ratio of volumes = 1 : 8

82. Two circular cylinders of equal volume have their heights in the ratio of 1 : 2. Ratio of their radii is:
  A.   √3 : 1
  B.   √5 : 1
  C.   2 : √3
  D.   √2 : 1
     
   
View Answer

Shortcut:
If the ratio of the heights of two circular cylinders of equal volume are given, then the ratio of their radii is given by the following result.
Ratio of radii = √(Inverse Ratio of the heights)
Here, Ratio of heights = 1 : 2
Using these values in the shortcut, we get:
Ratio of radii = √(2 : 1) = √2 : 1

83. Two circular cylinders of equal avolume have their height in the ratio of 1 : 2. Find the ratio of their curved surface areas.
  A.  1 : √2
  B.  2 : √3
  C.  1 : √3
  D.  2 : √5
     
   
View Answer

Shortcut:
If the ratio of curved surface areas of two circular cyinders of equal volume are given, then the ratio of their heights is given by the following result.
Ratio of curved surface areas = √(Ratio of the heights)
Note: If in place of cylinders, cones are given, this formula is applicable.
Here, Ratio of heights = 1 : 2
Using these values in the shortcut, we get:
Ratio of curved surface areas = √(1 : 2) = 1 : √2

84. Two circular cylinders of equal volume have their radii in the ratio of 1 : 2. Find the ratio of their curved surface areas.
  A.  2 : 3
  B.  2 : 1
  C.  2 : 5
  D.  1 : 4
     
   
View Answer

Shortcut:
If the ratio of radii of two circular cylinders of equal volume are given, then the ratio of their curved surface areas are given by the following result.
Ratio of curved surface areas = Inverse ratio of radii
Here, Ratio of radii = 1 : 2
Using these values in the shortcut, we get:
Ratio of curved surface areas = 2 : 1

85. Two circular cylinder of equal radii have their height in the ratio of 1 : 2. Find the ratio of their volumes.
  A.  1 : 3
  B.  1 : 4
  C.  1 : 5
  D.  1 : 2
     
   
View Answer

Shortcut:
If the ratio of heights of two circular cylinders of equal radii are given then the ratio of their volumes are given by the following result.
Ratio of volumes = Ratio of heights
Here, Ratio of heights = 1 : 2
Using these values in the shortcut, we get:
Ratio of volumes = 1 : 2

86. Two circular cylinders of equal radii have their height in the ratio of 1 : 2. Find the ratio of their curved surface areas.
  A.  1 : 2
  B.  1 : 8
  C.  1 : 4
  D.  1 : 9
     
   
View Answer

Shortcut:
If the ratio of heights of two circular cylinders of equal radii are given then the ratio of their curved surface area are given by the following result.
Ratio of curved surface area = Ratio of heights
Here, Ratio of heights = 1 : 2
Using these values in the shortcut, we get:
Ratio of curved surface area = 1 : 2

87. Two circular cylinders of equal radii have their volumes in the ratio of 3 : 1. Find the ratio of their curved surface areas.
  A.  3 : 2
  B.  2 : 3
  C.  3 : 1
  D.  3 : 5
     
   
View Answer

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

88. Two circular cylinder of equal height have their radii in the ratio of 2 : 3. Ratio of their volumes is.
  A.  9 : 16
  B.  4 : 9
  C.  9 : 2
  D.  4 : 1
     
   
View Answer

Shortcut:
If the ratio of radii of two circular cylinders of equal heights are given, then the ratio of their volume is given by the following result.
Ratio of volumes = (Ratio of radii)2
Here, Ratio of radii = 2 : 3
Using these values in the shortcut, we get:
Ratio of volumes = (2 : 3)2 = 4 : 9

89. Two circular cylinders of equal heights have their radii in the ratio of 2 : 3. Find the ratio of their curved surface areas.
  A.  2 : 9
  B.  4 : 9
  C.  2 : 5
  D.  2 : 3
     
   
View Answer

Shortcut:
If the ratio of radii of two circular cylinders of equal heights are given, then the ratio of their curved surface area is given by the following result.
Ratio of curved surface area = Ratio of radii
Here, Ratio of radii = 2 : 3
Using these values in the shortcut, we get:
Ratio of curved surface area = 2 : 3

90. Two curcular cylinders of equal heights have their curved surface areas in the ratio of 2 : 3. Find the ratio of their volumes.
  A.  2 : 5
  B.  1 : 7
  C.  4 : 9
  D.  5 : 3
     
   
View Answer

Shortcut:
If the ratio of curved surface area of two circular cylinders of equal heights are given, then the ratio of their volumes is given by the following result.
Ratio of volumes = (Ratio of curved surface area)2
Here, Ratio of curved surface area = 2 : 3
Using these values in the shortcut, we get:
Ratio of volumes = (2 : 3)2 = 4 : 9

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .