Mathematical Ability - Volume and Surface Area
Exam Duration: 45 Mins Total Questions : 25
The length of the longest pole that can be kept in a room 5 m long, 4 m broad and 3 m high, is:
- (a)
\(5\sqrt{2}\) m
- (b)
\(6\sqrt{2}\) m
- (c)
\(7\sqrt{2}\) m
- (d)
none of these
A solid metallic sphere of diameter 21 cm is melted and recasted into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed.
- (a)
503
- (b)
502
- (c)
501
- (d)
504
Find the volume and the surface area of the sphere of radius 5.6 cm.(π=22/7)
- (a)
735.9 cm3, 394.2 cm2
- (b)
733.0 cm3, 394.3 cm2
- (c)
735.2 cm3, 394.4 cm2
- (d)
700.9 cm3, 394.2 cm4
The product of the areas of three adjacent faces of a rectangular box is equal to:
- (a)
the volume of the box
- (b)
twice the volume of the box
- (c)
the square of the volume of the box
- (d)
cube root of the volume of the box
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of embankment.
- (a)
52.3 m
- (b)
53.3 m
- (c)
51.3 m
- (d)
53 m
The largest sphere is carved out of a cube of side 10 cm. Find the volume of the spheres.
- (a)
524.59 cm3
- (b)
523.60 cm3
- (c)
523.59 cm3
- (d)
523.58 cm3
A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it and spread all around to a width of 5 m to form an embankment. Find the height of embankment.
- (a)
4.67 m
- (b)
4.65 m
- (c)
4.64 m
- (d)
4.66 m
The diameter of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.
- (a)
8/3 cm
- (b)
8/2 cm
- (c)
7/3 cm
- (d)
1/2 cm
Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the flow of water is 72 cm per second how many litres of water are being pumped out in one hour?
- (a)
9979.2 litres
- (b)
9980.2 litres
- (c)
9979.3 litres
- (d)
9879 litres
If the diameter of the cross-section of a wire is decreased by 5%, how much per cent will the length be increased, so that the volume remains the same?
- (a)
\(\frac{360}{400}\)
- (b)
\(\frac{363}{400}\)
- (c)
\(\frac{361}{400}\)
- (d)
\(\frac{363}{401}\)
How many metres of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m.(Take π=22/7)
- (a)
100 m
- (b)
110 m
- (c)
109 m
- (d)
108 m
A rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder. (Take π=22/7)
- (a)
2700 cm3
- (b)
2771 cm3
- (c)
2772 cm3
- (d)
2770 cm3
The dimensions of a metallic cuboid are 100cm x 80 cm x 64 cm. It is melted and recast into a cube. Find the surface area of the cube.
- (a)
38400 cm2
- (b)
38401 cm2
- (c)
38404 cm2
- (d)
38990 cm2
If each side of a cube of volume V is doubled, its volume becomes k V, where k is equal to:
- (a)
8
- (b)
4
- (c)
2
- (d)
14
Capacity of a cylindrical vessel is 25.872 litres. If the height of the cylindrical is three times the radius of its base, what is the area of the base?
- (a)
336 cm2
- (b)
1232 cm2
- (c)
616 cm2
- (d)
none of these
Find the number of coins 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
- (a)
449
- (b)
448
- (c)
440
- (d)
450
Three cubes of metal, whose edges are 6 cm, 8 cm and 10 cm, are melted and one new cube made. Find the total surface area of the new cube.
- (a)
864 cm2
- (b)
862 cm2
- (c)
860 cm2
- (d)
86.4 cm2
A hemispherical tank of radius \(1\frac{3}{4}\) is full of water. It is connected with a pipe which empties it at the rate of 7 litres per second. How much time will it take to empty the tank completely?
- (a)
25.73 min
- (b)
24.70 min
- (c)
26.73 min
- (d)
26.74 min
If the radius of a sphere is doubled, its surface area will increase by:
- (a)
50%
- (b)
200%
- (c)
300%
- (d)
400%
The diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
- (a)
\(\frac{1}{62}\)
- (b)
\(\frac{1}{64}\)
- (c)
\(\frac{1}{60}\)
- (d)
\(\frac{1}{65}\)
The sum of the radius of the base and the height of a solid cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the volume of the cylinder. (Take π=22/7)
- (a)
4620 cm3
- (b)
4620 cm2
- (c)
4621 cm3
- (d)
4621 cm2
Surface area of a sphere and curved surface area of a right circular cylinder that just encloses the sphere. Then
- (a)
sphere area of sphere> curved surface of cylinder
- (b)
sphere area of sphere < curved surface of cylinder
- (c)
sphere area of sphere = curved surface of cylinder
- (d)
none of these
How many cubes of 10 cm edge can be put in a cubic box of 1m edge?
- (a)
10
- (b)
100
- (c)
1000
- (d)
10000
A sphere of radius 3 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is submerged completely, by how much will the surface of water be raised?
- (a)
2
- (b)
3
- (c)
4
- (d)
1
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
- (a)
6:π
- (b)
3:π
- (c)
4:π
- (d)
5:π