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111. The length, breadth and height of a cuboid are made 3, 4, and 5 times respectively. Find the percentage increase in its volume.
  A.  6200%
  B.  5900%
  C.  5200%
  D.  5500%
     
   
View Answer

Shortcut:
If length, breadth and height of a cuboid are 'a', 'b' and 'c' times respectively, then
Increase in volume = [(abc − 1) x 100] per cent
[Note:
(i) If any of the sides of a cuboid is made 'a' times, then the percentage increase in its volume is (a − 1) x 100]
(ii) If any two of the sides of a cuboid are made 'a' and 'b' times, then the percentage increase in its volume is = [(ab − 1) x 100] per cent]
Here, a = 3, b = 4, c = 5
Using these values in the shortcut, we get:
Increase in volume = [(3 x 4 x 5 − 1) x 100]
= [(60 − 1) x 100]% = 5900%

112. If length and breadth of a cuboid are made 2 and 3 times respectively. Find the percentage increase in its volume.
  A.   500%
  B.   400%
  C.   450%
  D.   550%
     
   
View Answer

Shortcut:
If length, breadth and height of a cuboid are 'a', 'b' and 'c' times respectively, then
Increase in volume = [(abc − 1) x 100] per cent
[Note:
(i) If any of the sides of a cuboid is made 'a' times, then the percentage increase in its volume is (a − 1) x 100]
(ii) If any two of the sides of a cuboid are made 'a' and 'b' times, then the percentage increase in its volume is = [(ab − 1) x 100] percent]
Here, a = 2, b = 3
Using these values in the shortcut, we get:
Increase in volume = [(2 x 3 − 1) x 100]
= [(6 − 1) x 100]% = 500 %

113. If length of a cuboid are made 4 times respectively. Find the percentage increase in its volume.
  A.  350%
  B.  400%
  C.  200%
  D.  300%
     
   
View Answer

Shortcut:
If length, breadth and height of a cuboid are 'a', 'b' and 'c' times respectively, then
Increase in volume = [(abc − 1) x 100] per cent
[Note:
(i) If any of the sides of a cuboid is made 'a' times, then the percentage increase in its volume is (a − 1) x 100]
(ii) If any two of the sides of a cuboid are made 'a' and 'b' times, then the percentage increase in its volume is = [(ab − 1) x 100] per cent]
Here, a = 4
Using these values in the shortcut, we get:
Increase in volume = [(4 − 1) x 100]
= [(3 − 1) x 100]% = 300 %

114. Each edge of a cube is made 2 times. Find
(i) the percentage increase in its volume and
(ii) the percentage increase in its total surface area.
  A.  500% ; 300%
  B.  700% ; 400%
  C.  700% ; 300%
  D.  500% ; 400%
     
   
View Answer

Shortcut:
If side of a cube is made 'z' times, then
(i) the percentage increase in its volume is [(z3 − 1) x 100] per cent
(ii) the percentage increase in its total surface area is [(z2 − 1) x 100] percent
Here, z = 2
Using these values in the shortcut, we get:
(i) Increase in volume = [(23 − 1) x 100] per cent
= [(8 − 1) x 100]% = 700 %
(ii) the percentage increase in its total surface area is [(22 − 1) x 100] per cent
= [(4 − 1) x 100] = 300 %
115. Each edge of a cube is increased by 50%. What is the percentage increase in its volume?
  A.  240.5%
  B.  237.5%
  C.  247.5%
  D.  230.5%
     
   
View Answer

Shortcut:
If side of a cube is increased by a%, then its volume increases by
[
3a +
3a2 / 100
+
a3 / 1002
]
%
or
[(
1 +
a / 100
)
3 − 1
]
x 100%
[Note: for decrease put the −ve value of a.]
Here, a = 50
Using these values in the shortcut, we get:
Increase in volume =
[
3 x 50 +
3 x 502 / 100
+
503 / 1002
]
%
=
[
150 +
3 x 50 x 50 / 100
+
50 x 50 x 50 / 100 x 100
]
%
=
[
150 + 3 x 5 x 5 +
125 / 10
]
%
= (150 + 75 + 12.5)% = 237.5%

116. Each edge of a cube is increased by 50%. What is the percentage increase in its surface area?
  A.  145%
  B.   135%
  C.   125%
  D.   135%
     
   
View Answer

Shortcut:
If side of a cube is increased by a%, then its surface area increases by
(
2a +
a2 / 100
)
per cent.
[Note:
(1) For the area, we see that only two measuring sides are involved (as area has 2-dimensions). So, we use the above formula.
(2) For decrease put the −ve value of a.]
Here, a = 50
Using these values in the shortcut, we get:
Increase in surface area =
(
2 x 50 +
502 / 100
)
%
=
(
100 +
50 x 50 / 100
)
% = (100 + 25)% = 125%

117. The diameter of a sphere is increased by 25 per cent. What is the per cent increase in its volume?
  A.  85.25%
  B.  99.31%
  C.  92.25%
  D.  95.31%
     
   
View Answer

Shortcut:
If the radius (or diameter) of a sphere or a hemi-shpere is changed by a%, then its volume changes by
[
3a +
3a2 / 100
+
a3 / 1002
]
%
or
[(
1 +
a / 100
)
3 − 1
]
x 100%
[Note: for decrease put the −ve value of a.]
Here, a = 25
Using these values in the shortcut, we get:
Increase in volume =
[
3 x 25 +
3 x 252 / 100
+
253 / 1002
]
%
=
[
75 +
3 x 25 x 25 / 100
+
25 x 25 x 25 / 100 x 100
]
%
= (75 + 18.75 + 1.5625)% = 95.31%

118. The diameter of a hemisphere is increased by 25%. What is the percentage increase in its curved surface area.
  A.   46.25%
  B.   56.25%
  C.   64.25%
  D.   52.75%
     
   
View Answer

Shortcut:
If the radius (or diameter) of a sphere or a hemi-sphere is changed by a%, then its curved surface area changes by
(
2a +
a2 / 100
)
percent.
Here, a = 25
Using these values in the shortcut, we get:
Change in curved surface area = 2 x 25 +
252 / 100
%
= 50 +
25 x 25 / 100
% = (50 + 6.25)% = 56.25%

119. The height of a cylinder is decreased by 25%. Keeping its radius unchanged. What is the per cent change in tis volume?
  A.  25%
  B.  15%
  C.  35%
  D.  50%
     
   
View Answer

Shortcut:
If height of a right circular cylinder is changed by a% and radius remains the same then its volume changes by a%.
Here, a = 25
Using these values in the shortcut, we get:
Change in volume = 25%

120. The radius of a cylinder is increased by 25%. Keeping its height unchanged. What is the percentage increase in its volume?
  A.  58.35%
  B.  46.25%
  C.  56.25%
  D.  52.25%
     
   
View Answer

Shortcut:
If the radius of a right circular cylinder is changed by a% and height remains the same the volume changes by
(
2a +
a2 / 100
)
per cent.
or
[(
1 +
a / 100
)
2 − 1
]
per cent.
Here, a = 25
Using these values in the shortcut, we get:
Increase in volume =
(
2 x 25 +
252 / 100
)
percent.
=
(
50 +
25 x 25 / 100
)
% = (50 + 6.25)% = 56.25%

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