Quantitative Aptitude - Volume and Surface Areas
Exam Duration: 60 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
A boat having a length 3 m and breadth 2 m is floating on a lake. the boat sinks by 1 cm when a man gets on it. The mass of man is :
- (a)
12 kg
- (b)
60 kg
- (c)
72 kg
- (d)
96 kg
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
A hall is 15 m long and 12 m broad. if the sum of the area of the floor and the ceiling is equal to the sum of areas of the four walls, the volume of the hall is :
- (a)
720
- (b)
900
- (c)
1200
- (d)
1800
A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. it surface area is :
- (a)
208 cm2
- (b)
270 cm2
- (c)
360 cm2
- (d)
408 cm2
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
Total surface area of a cube whose side is 0.5 cm is :
- (a)
\(\frac { 1 }{ 4 } \) cm2
- (b)
\(\frac { 1 }{ 8 } \) cm2
- (c)
\(\frac { 3 }{ 4 } \)cm2
- (d)
\(\frac { 3 }{ 2 } \)cm2
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
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
Five equal cubes, each of side 5 cm, are placed adjacent to each other. The value of the new solid formed will be :
- (a)
125 cm3
- (b)
625 cm3
- (c)
15525 cm3
- (d)
None of these
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
The volume of two cubes are in the ratio 8 : 27. The ratio of their surface area is :
- (a)
2 : 3
- (b)
4 : 9
- (c)
12 : 9
- (d)
None of these
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
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
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
The length of the canvas 1.1 m wide required to build a conical tent 14 m and the floor area 346.5 sq m is :
- (a)
490 m
- (b)
525 m
- (c)
665 m
- (d)
860 m
Two cones have their heights in the ratio of 1 : 3 and radii 3 : 1. The ratio of their volume is :
- (a)
1 : 1
- (b)
1 : 3
- (c)
3 : 1
- (d)
2 : 3
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. Then radius of the cone will be :
- (a)
4 cm
- (b)
5 cm
- (c)
6 cm
- (d)
8 cm
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
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
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
If the surface area of two sphere are in the ratio of 4 : 25, then the ratio of their volume is :
- (a)
4 : 25
- (b)
25 : 4
- (c)
125 : 8
- (d)
8 : 125
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
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
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
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
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.
A solid metallic cone is melted and recast into a sphere.What is the radius of the sphere ?
I. The radius of the base of the cone is 2.1 cm.
II.The height of the cone is four times the radius of its base.
III.The height of the cone is 8.4 cm.
- (a)
Only I and II
- (b)
Only II and III
- (c)
Only I and III
- (d)
Any two of the three
- (e)
All I,II and III