TNPSC Quantitative Aptitude - Volume and Surface Areas
Exam Duration: 45 Mins Total Questions : 30
A cistern 6 m long and 4m wide contain water up to a depth of 1 m 25 cm. the total area of the wet surface is :
- (a)
49 m2
- (b)
50 m2
- (c)
53.5 m2
- (d)
55 m2
How many bricks, each measuring 25 cm \(\times \) 11.25 cm \(\times \) 6 cm, will be needed to build a wall 8 m \(\times \) 6 m \(\times \) 22.5 cm ?
- (a)
5600
- (b)
6000
- (c)
6400
- (d)
7200
An open box is made of wood 3 cm thick. Its external dimensions are 1.46m, 1.16 m and 8.3 dm, The cost of painting the inner surface of the box at 50 paise per 100 sq cm is :
- (a)
Rs. 138.50
- (b)
Rs. 277
- (c)
Rs.415.50
- (d)
Rs. 554
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
If the areas of the three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu.cm; then the length of the shortest side is :
- (a)
10 cm
- (b)
15 cm
- (c)
20 cm
- (d)
30 cm
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
A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical blocks each of edge 20 cm that can be packed inside the box is :
- (a)
30
- (b)
53
- (c)
60
- (d)
120
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
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
The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60 cm is :
- (a)
2 : 1
- (b)
3 : 2
- (c)
4 : 3
- (d)
5 : 3
The height of a closed cylinder of given volume and the minimum surface area is :
- (a)
equal to its diameter
- (b)
half of its diameter
- (c)
double of its diameter
- (d)
none of these
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
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
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
A well with 14 m inside diameter is dug 10 m deep. Earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. The height of the embankment is
- (a)
\(\frac {1} {2} \) m
- (b)
\( \frac {2} {3} \)
- (c)
\( \frac {3} {4} \)
- (d)
\( \frac {3} {5} \)m
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
- (a)
84
- (b)
90
- (c)
168
- (d)
336
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
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
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
The curved surface area of sphere is 5544 sq.cm. Its volume is :
- (a)
22176 cm3
- (b)
33951 cm3
- (c)
38808 cm3
- (d)
42304 cm3
If the measured value of the radius is 1.5% larger, the percentage error(correct to one decimal place ) made in calculating the volume of a sphere is :
- (a)
2.1
- (b)
3.2
- (c)
4.6
- (d)
5.4
A solid metalic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. The number of spherical balls, thus obtained is :
- (a)
16
- (b)
48
- (c)
64
- (d)
82
A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of those are 15 cm and 2 cm respectively. The diameter of the third ball is :
- (a)
2.5 cm
- (b)
2.66 cm
- (c)
3 cm
- (d)
3.5 cm
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 cylindrical vessel of radius 4 cm contain water. A solid sphere of radius 3 cm is lowered into the water untill it is completely immersed. The water level in the vessel will rise by :
- (a)
\(\frac { 2 }{ 9 } \) cm
- (b)
\(\frac { 4 }{ 9 } \) cm
- (c)
\(\frac { 9 }{ 4 } \) cm
- (d)
\(\frac { 9 }{ 2 } \) cm
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
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
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 weight of the iron beam ?
I. The beam is 9 m long, 40 cm wide and 20 cm high.
II. Iron weighs 50 kg per cubic metre.
- (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
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 total cost of painting the inner surface of an open box at the rate of 50 paise per 100 sq.cm ?
I. The box is made of wood 3 cm thick.
II. The external dimensions of the box are 50 cm, 40 cm and 23 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
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