Quantitative Aptitude - Volume and Surface Areas
Exam Duration: 45 Mins Total Questions : 30
The capacity of a tank of dimension (8 m \(\times \) 6 m \(\times \) 2.5 m ) is :
- (a)
120 litres
- (b)
1200 liters
- (c)
12000 litres
- (d)
120000 litres
Given that 1 cu. cm of marbles weights 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is :
- (a)
26.5 cm
- (b)
32 cm
- (c)
36 cm
- (d)
37.5 cm
The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2 . The volume of the cubiod is :
- (a)
24 cm3
- (b)
48 cm3
- (c)
64 cm3
- (d)
120 cm3
The maximum length of the pencil that can be kept in a rectangular box of dimensions 8 cm \(\times \) 6 cm , is :
- (a)
\(2\sqrt { 13 } \) cm
- (b)
\(2\sqrt { 14 } \) cm
- (c)
\(2\sqrt { 26 } \) cm
- (d)
\(10\sqrt { 2 } \) cm
50 men took dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be :
- (a)
20 cm
- (b)
25 cm
- (c)
35 cm
- (d)
50cm
The cost of the paint is Rs 36.50 per kg. if 1 kg of paint covers 16 square feet, now much will it cost to paint outside of a cube having 8 feet each side ?
- (a)
RS. 692
- (b)
Rs. 768
- (c)
Rs. 876
- (d)
Rs. 972
- (e)
None of these
The surface area of a cube is 600 cm2 . The length of its diagonal is :
- (a)
\(\frac { 10 }{ \sqrt { 3 } } \) cm
- (b)
\(\frac { 10 } { \sqrt { 2 } }\) cm
- (c)
\(10\sqrt { 2 }\) cm
- (d)
\(10\sqrt { 3 }\) cm
If the numbers representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be :
- (a)
3
- (b)
4
- (c)
5
- (d)
6
How many cubes of 10 cm edges can be put in a cubical box of 1 m edges ?
- (a)
10
- (b)
100
- (c)
1000
- (d)
10000
The size of a wooden block of 5 \(\times\) 10 \(\times\) 20 cm is cut p into an excat number of equal cubes. How nmany such blocks will be required to construct a solid wooden cuve of minimum size ?
- (a)
6
- (b)
8
- (c)
12
- (d)
16
Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is :
- (a)
12 cm
- (b)
14 cm
- (c)
16 cm
- (d)
18 cm
A cube of edge 5 cm is cut into cubes each of edge 1 cm. the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
- (a)
1 : 5
- (b)
1 : 25
- (c)
1 : 125
- (d)
1 : 625
A large cube is formed from the material obtained by melting three smaller cubes of 3,4 and 5 cm side. What is the ratio of the total surface area of the smallest cubes and the large cube ?
- (a)
2 : 1
- (b)
3 : 2
- (c)
25 : 18
- (d)
27 : 20
If each edge of a cube is increased by 25%, then the percentage increase in its surface area is :
- (a)
20%
- (b)
48.75%
- (c)
50%
- (d)
56.25%
A circular well with a diameter of 2 metres, is dug to a depth of of 14 metres. What is the volume of the earth dug out ?
- (a)
32 m3
- (b)
36 m3
- (c)
40 m3
- (d)
44 m3
If the volume of a right circular cylinder with its height equal to the radius is \(25 \frac {1 } {7}\) cm3, Then the radius of the cylinder is equal to :
- (a)
\(\pi\) cm
- (b)
2 cm
- (c)
3 cm
- (d)
4 cm
A closed metallic cylindrical box is 1.25 m high and its base radius is 35 cm. If the sheet metal cost Rs. 80 m2, the cost of the material used in the box is :
- (a)
Rs. 281.60
- (b)
Rs. 290
- (c)
Rs. 340.50
- (d)
Rs. 500
Two right circular cylinder of equal volume have their heights in the ratio 1 : 2. the ratio of their radii is :
- (a)
1 : 2
- (b)
1 : 4
- (c)
2 : 1
- (d)
\(\sqrt { 2 }\) : 1
A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal everywhere is 0.4 cm thick. The volume of the metal is :
- (a)
280.52 cm3
- (b)
306.24 cm3
- (c)
36 kg
- (d)
36.9 kg
The radius of the base and the height of a cone are 3 cm and 5 cm respectively whereas the radius of the base and the height of the cylinder are 2 cm and 4 cm respectively. The ratio of the volume of the cone to that of the cylinder is :
- (a)
1 : 3
- (b)
15 : 8
- (c)
15 : 16
- (d)
45 : 16
If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area of its curved surface is :
- (a)
154 cm2
- (b)
550 cm2
- (c)
704 cm2
- (d)
1254 cm2
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, the ratio of the total surface area of the cylinder to that of the cone is :
- (a)
3 : 1
- (b)
13 : 9
- (c)
17 : 9
- (d)
34 : 9
Consider the volumes of the following :
1. A parallelopiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm
- (a)
1,2,3,4
- (b)
1,3,2,4
- (c)
4.2.3.1
- (d)
4,3,2,1
The volumes of two sphere are in the ratio of 64:27. The ratio of their surface area is :
- (a)
1:2
- (b)
2:3
- (c)
9:16
- (d)
16:9
The volume of the greatest sphere that can be off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
- (a)
\(\frac { 4 }{ 3 } \)\(\pi\)
- (b)
\(\frac { 10 }{ 3 } \pi \)
- (c)
\(5\pi \)
- (d)
\(\frac { 20 }{ 3 } \pi \)
The diameter of a sphere is 8 cm. It is melted and drawn into a wire of diameter 3 mm. The length of the wire is :
- (a)
36.9 m
- (b)
37.9 m
- (c)
38.9 m
- (d)
39.9 m
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is :
- (a)
\(\sqrt { 3 }\) cm
- (b)
2 cm
- (c)
3 cm
- (d)
4 cm
A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
- (a)
25%
- (b)
25\(\pi\)%
- (c)
50%
- (d)
75%
Volume of a hemisphere is 19404 cu.cm. Its radius is :
- (a)
10.5 cm
- (b)
17.5 cm
- (c)
21 cm
- (d)
42 cm
The capacities of two hemispherical vessels are 6.4 litres and 21.6 lites.The areas of inner curved surface of vessels will be in the ratio of :
- (a)
\(\sqrt { 2 } :\sqrt { 3 } \)
- (b)
2 : 3
- (c)
4 : 9
- (d)
16 : 81