Volume and Surface Areas
Exam Duration: 45 Mins Total Questions : 30
Find the surface area of a 10 cm \(\times \)4 cm \(\times \) 3 cm brick
- (a)
84 sq.cm
- (b)
124 sq.cm
- (c)
164 sq.cm
- (d)
180sq.cm
The area of the base of a rectangular tank is 6500 cm2 and the volume of water contained in it is 2.6 cubic metres. The depth of water in the tank is :
- (a)
3.5 m
- (b)
4 m
- (c)
5 m
- (d)
6 m
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
Half cubic metre of gold sheet is extended by hammering so as to cover an area of 1 hectare. The thickness of the sheet is :
- (a)
0.0005 cm
- (b)
0.005 cm
- (c)
.05 cm
- (d)
0.5 cm
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
Find the length of the longest rod that can be placed in a room 16 m long, 12 m broad and \(10\frac { 2 }{ 3 } \) m high
- (a)
\(22\frac { 1 }{ 3 } \) m
- (b)
\(22\frac { 2 }{ 3 } \) m
- (c)
22 m
- (d)
68 m
A tank 4 m long, 2.5 m wide and 1.5 m deep is dug in a field 31 m long and 10 m wide. If the earth dug out is evenly spread out over the field, the rise in level of the field is :
- (a)
3.1 cm
- (b)
4.8 cm
- (c)
5 cm
- (d)
6.2 cm
A metallic sheet is of rectangular shape with dimensions 48 m \(\times\) 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is :
- (a)
4830
- (b)
5120
- (c)
6420
- (d)
8960
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is :
- (a)
90 cm
- (b)
1 dm
- (c)
1 m
- (d)
1.1 m
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 cost of painting the whole surface area of a cube at the rate of 13 paise per sq. cm is Rs. 343.98. Then the volume of the cube is :
- (a)
8500 cm3
- (b)
9000 cm3
- (c)
9250 cm3
- (d)
9261 cm3
The length of an edge of a hollow cube open at one face is \(\sqrt { 3 } \) metres. what is the length of the largest pole that it can accommodate ?
- (a)
\(\sqrt { 3 } \) metres
- (b)
3 metres
- (c)
\(3\sqrt { 3 }\) metres
- (d)
\(\frac { 3 }{ \sqrt { 3 } } \) metres
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 each edge of a cubiod is doubled, then its volume :
- (a)
is doubled
- (b)
become 4 times
- (c)
become 6 times
- (d)
become 8 times
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 volume of a right circular cylinder whose curved surface area is 2640 cm2 and circumference of its base is 66 cm, is :
- (a)
3465 cm3
- (b)
7720 cm3
- (c)
13860 cm3
- (d)
55440 cm3
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 slant height of a conical is 2.5 km and the area of its base is 1.54 km2. The height of the mountain is :
- (a)
2.2 km
- (b)
2.4 km
- (c)
3 km
- (d)
3.11 km
If the radius and height of a right circular cone are increased by 20%, its volume will be increased by :
- (a)
2 times
- (b)
3 times
- (c)
4 times
- (d)
8 times
If both the radius and height of a right circular cone are increased by 20%, its volume will be increased by :
- (a)
20 %
- (b)
40 %
- (c)
60 %
- (d)
72.8 %
Surface area of a sphere is 2464 cm2. If its radius be doubled, then the surface area of the new sphere will be :
- (a)
4928 cm2
- (b)
9856 cm2
- (c)
19721 cm2
- (d)
data insusufficient
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 the sphere is increased by 2 cm, then its surface area increased by 352 cm2. The radius of the sphere before the increase was :
- (a)
3 cm
- (b)
4 cm
- (c)
5 cm
- (d)
6 cm
If three metallic spheres of radill 6 cms, 8 cms and 10 cms are melted to form a single sphere, the diameter of the new sphere will be :
- (a)
12 cms
- (b)
24 cms
- (c)
30 cms
- (d)
36 cms
A solid piece of iron of dimensions 49 \(\times\) 33 \(\times\) 24 cm is moulded into a sphere. The radius of the sphere is :
- (a)
21 cm
- (b)
28 cm
- (c)
35 cm
- (d)
None of these
The surface area of the sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is :
- (a)
3 cm
- (b)
4 cm
- (c)
6 cm
- (d)
12 cm
A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are there ?
- (a)
108
- (b)
120
- (c)
144
- (d)
180
In what ratio are the volume of a cylinder, a cone and a sphere, if each has the same diameter and the same height ?
- (a)
1 : 2 : 3
- (b)
2 : 3 : 1
- (c)
3 : 1 : 2
- (d)
3 : 2 : 1
A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is :
- (a)
1.4 cm
- (b)
2 cm
- (c)
2.4 cm
- (d)
4.2 cm
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the capacity of the cylindrical tank ?
I.The area of the base is 64,600 sq.cm.
II.The height of the tank is 1.5 times the radius.
III.The circumference of base is 880 cm.
- (a)
Only I and II
- (b)
Only II and III
- (c)
Only I and III
- (d)
Any two of the three
- (e)
Only II and either I or III