Quantitative Aptitude - Volume and Surface Areas
Exam Duration: 45 Mins Total Questions : 30
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 volume of a rectangular block of stone is 10368 dm3. Its dimensions are in the ratio of 3 : 2 : 1. If its entire surface is polished at 2 paise per dm2. then the total cost will be :
- (a)
31.50
- (b)
31.68
- (c)
69
- (d)
63.36
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
The number of bricks,each measuring 25 cm \(\times \) 12.5 cm \(\times \) 7.5 cm , required to construct a wall 6 m long, 5 m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is :
- (a)
3040
- (b)
5740
- (c)
6080
- (d)
8120
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
If the areas of the three adjacent faces of a cuboidal box are 120 cm2, 72 cm2 and 60 cm2 respectively, then find the volume of the box
- (a)
720 cm2
- (b)
864 cm2
- (c)
7200 cm2
- (d)
(72)2 cm2
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 dimensions of a piece of iron in the shape of a cubiod are 270 cm \(\times\) 100 cm \(\times\) 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :
- (a)
14400 cm2
- (b)
44200 cm2
- (c)
57600 cm2
- (d)
86400 cm2
If the volume of the cube is 729 cm3, then the surface area of the cube will be :
- (a)
450 cm2
- (b)
466 cm2
- (c)
476 cm2
- (d)
486 cm2
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%
The capacity of a cylindrical tank is 246.4 litres, If the height is 4 metres, what is the diameter of the base ?
- (a)
1.4 m
- (b)
2.8 m
- (c)
14 m
- (d)
28 m
- (e)
None of these
How many cubes of 3 cm edges can be cut out of a cube of 18 cm edges ?
- (a)
36
- (b)
216
- (c)
208
- (d)
432
The radii of two cylinder are in the ratio of 2 : 3 and their height are in the ratio of 5 : 3. The ratio of their volume is :
- (a)
4 : 9
- (b)
9 : 4
- (c)
20 : 27
- (d)
27 : 20
X and Y are two cylinder of the same height. The base of X has diameter that is half the diameter of the base of Y. If the height of X id doubled, the volume of X becomes :
- (a)
equal to the volume of Y
- (b)
double the volume of Y
- (c)
half the volume of Y
- (d)
greater than the volume of Y
The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is :
- (a)
460
- (b)
500
- (c)
600
- (d)
640
What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm , 0.25 cm thick and 15 cm long ?
- (a)
42.3215 cm
- (b)
44.0123 cm
- (c)
44.0625 cm
- (d)
44.6023 cm
A circular cylinder can hold 61.6 c.c of water. If the height of the cylinder is 40 cm and the outer diameter is 16 mm, the thickness of the material of the cylinder is :
- (a)
0.2 mm
- (b)
0.3 mm
- (c)
1 mm
- (d)
2 mm
A right triangle with side 3 cm, 4cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is :
- (a)
12\(\pi\) cm3
- (b)
15 \(\pi\) cm3
- (c)
16\(\pi\) cm3
- (d)
20\(\pi\) cm3
Volume of a right circular cone having base radius 70 cm and curved surface area 40040 cm2 is :
- (a)
823400 cm3
- (b)
824000 cm3
- (c)
840000 cm3
- (d)
862400 cm3
If both height of a right circular cone is increased by 200% and the radius of the base is reduced by 50 %, then the volume of the cone :
- (a)
remains unaltered
- (b)
decrease by 25 %
- (c)
increase by 25 %
- (d)
increase by 50 %
A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm\(\times\)5 cm \(\times\) 2 cm. The percentage of wood wasted is :
- (a)
34%
- (b)
46%
- (c)
54%
- (d)
66%
A solid metalic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Then number of cone is :
- (a)
450
- (b)
1350
- (c)
4500
- (d)
13500
If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the sphere is :
- (a)
9 cm
- (b)
36 cm
- (c)
54 cm
- (d)
81 cm
Spheres A and B have their radill 40 cm and 10 cm respectively. The ratio of the surface area of A to the surface area of B is :
- (a)
1 : 4
- (b)
1 : 16
- (c)
4 : 1
- (d)
16 : 1
If the radius of a sphere is doubled, how many times does its volume become ?
- (a)
2 times
- (b)
4 times
- (c)
6 times
- (d)
8 times
How many spherical bullets can be made out of lead cylinder. 15 cm high and width base radius 1 cm and height 5 cm is :
- (a)
6000
- (b)
6480
- (c)
7260
- (d)
7800
A cylindrical rod of iron whose hight is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. The number of spherical balls is :
- (a)
12
- (b)
16
- (c)
24
- (d)
48
A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then :
- (a)
H = 2R
- (b)
H = 3R
- (c)
H = \(\sqrt 3R \)
- (d)
H = \(\frac { 2 }{ 3 } R\)
A hemisphere and a cone have equal bases. If their height are also equal, then the ratio of their curved surface will be :
- (a)
1 : 2
- (b)
2 : 1
- (c)
1 : \(\sqrt { 2 } \)
- (d)
\(\sqrt { 2 } \) : 1
Each of the questions given below consists of a statements and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the given question. Read both the statements
What is the height of a circular cone ?
I. The area of that cone is equal to the area of a rectangular whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm
- (a)
If the data in the statement I alone are sufficient to answer the question, while the data in the statement II alone are not sufficient to answer the question
- (b)
If the data in the statement II alone are sufficient to answer the question, while the data in the statement I alone are not sufficient to answer the question
- (c)
If the data either in statement I or in statement II alone are sufficient to answer the question
- (d)
If the data even in both statement I and II together are not sufficient to answer the question:
- (e)
If the data in both statement I and II together are necessary to answer the questions