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
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
A rectangular water tank is 80 m \(\times \) 40 m. water flows into it through a pipe 40 sq.cm at the opening at a speed of 10 km/hr. how much, the water level will rise in the tank in half an hour ?
- (a)
\(\frac { 3 }{ 2 } \) cm
- (b)
\(\frac { 4 }{ 9 } \) cm
- (c)
\(\frac { 5 }{ 8 } \) cm
- (d)
none of these
The sum of the length, breadth and depth of a cubiod is 19 cm and its diagonal is \(5\sqrt { 5 } \) cm. it surface area is :
- (a)
125 cm2
- (b)
286 m2
- (c)
361 m2
- (d)
486 m2
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
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
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
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 perimeter of one face a of cube is 20 cm. Its volume must be :
- (a)
125 cm3
- (b)
400 cm3
- (c)
1000 cm3
- (d)
8000 cm3
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
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
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
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
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 height of a right circular cylinder is 14 cm and its curved surface is 704 sq.cm. Then its volume is :
- (a)
1408 cm3
- (b)
2816 cm3
- (c)
5632 cm3
- (d)
9856 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 radius of a wire is decreased to one-third and its volume remains the same. The new length is how many times the original length ?
- (a)
1 times
- (b)
3 times
- (c)
6 times
- (d)
9 times
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
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
- (a)
30\(\pi\) m2
- (b)
40\(\pi\) m2
- (c)
60\(\pi\) m2
- (d)
80\(\pi\) m2
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
The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
- (a)
13.6 cm3
- (b)
89.8 cm3
- (c)
121 cm3
- (d)
147.68 cm3
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
How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm \(\times\) 11 cm\(\times\)12 cm ?
- (a)
7200
- (b)
8400
- (c)
72000
- (d)
84000
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 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 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 volume of a cube ?
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.
- (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
Is a given rectangular block, a cube ?
I. At least 2 faces of the rectangular block are squares.
II.The volume of the block is 64.
- (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
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