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Quiz 6
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Q.1
The dimensions of a certain machine are 48" × 30" × 52". If the size of the machine is increased proportionately until the sum of its dimensions equal 156", what will be the increase in the shortest side ?
4"
6"
8"
9"
Q.2
How many small cubes, each of 96 cm surface area, can be formed from the material obtained by melting a larger cube of 384 cm surface area ?
5
8
800
8000
Q.3
The length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 sq.m is :
490 m
525 m
665 m
860 m
Q.4
The radius of a hemispherical bowls is 6 cm. The capacity of the bowl is $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
495.51 cm
^{3}
452.57 cm
^{3}
345.53 cm
^{3}
422 cm
^{3}
Q.5
A hemispherical bowl is 176 cm round the brim. Supposing it to be half full, how many persons may be served from it in hemispherical glasses 4 cm in diameter at the top ?
1172
1272
1372
1472
Q.6
A closed metallic cylindrical box is 1.25 m high and its base radius is 35 cm. If the sheet metal costs Rs. 80 per m
^{2}
, the cost of the material used in the box is :
Rs. 281.60
Rs. 290
Rs. 340.50
Rs. 500
Q.7
A well with inner diameter 8 m is dug 14 m deep. Earth take out of its has been evenly spread all around it to a width of 3 m form an embankment. The height of the embankment will be :
$${\text{4}}\frac{{26}}{{33}}{\text{m}}$$
$${\text{5}}\frac{{26}}{{33}}{\text{m}}$$
$${\text{6}}\frac{{26}}{{33}}{\text{m}}$$
$${\text{7}}\frac{{26}}{{33}}{\text{m}}$$
Q.8
An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe is :
3068 cm
^{2}
3168 cm
^{2}
3268 cm
^{2}
3368 cm
^{2}
Q.9
A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface will be :
$$\sqrt 2 :1$$
$$1:\sqrt 2 $$
2 : 1
1 : 2
Q.10
Diameter of a jar cylindrical in shape is increased by 25%. By what percent must the height be decreased so that there is no change in its volume :
10%
25%
36%
50%
Q.11
Water is flowing at the rate of 5 km/hr through a cylindrical pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm :
1 hour
$$1\frac{1}{2}$$ hours
2 hours
3 hours
Q.12
Water flows at the rate of 10 metres per minutes from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?
48 minutes 15 seconds
51 minutes 12 seconds
52 minutes 1 seconds
55 minutes
Q.13
A well has to be dug out that is to be 22.5 m deep and of diameter 7 m. Find the cost of plastering the inner curved surface at Rs. 3 per sq.meter :
Rs. 1465
Rs. 1475
Rs. 1485
Rs. 1495
Q.14
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be :
12 cm
24 cm
30 cm
36 cm
Q.15
A right circular cylinder and a sphere are of equal volumes and their radii are also equal. If h is the height of the cylinder and d, the diameter of the sphere, then :
$$h = d$$
$$2h = d$$
$$\frac{h}{3} = \frac{d}{2}$$
$$\frac{h}{2} = \frac{d}{3}$$
Q.16
A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is :
3 : 2
4 : 1
4 : 3
7 : 4
Q.17
If the radius of a sphere is doubled, how many times does its volume becomes ?
2 times
4 times
6 times
8 times
Q.18
The volume of two spheres are in the ratio of 64 : 27. The ratio p their surface areas is :
1 : 2
2 : 3
9 : 16
16 : 9
Q.19
A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by :
$$10\frac{1}{2}{\text{ cm}}$$
$$11\frac{3}{7}{\text{ cm}}$$
$$12\frac{6}{7}{\text{ cm}}$$
$$14{\text{ cm}}$$
Q.20
A rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m by 2.5 m. The earth dug out is evenly spread over the remaining portion of the field. How much is the level of the field raised ?
4 m
4.1 m
4.2 m
4.3 m
Q.21
If the areas of three adjacent faces of a cuboid are x, y, z respectively, then the volume of the cuboid is :
$$xyz$$
$$2xyz$$
$$\sqrt {xyz} $$
$$3\sqrt {xyz} $$
Q.22
A plot of land in the form of a rectangle has dimensions 240 m × 180 m. A drain-let 10 m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drain-let is :
1.223 m
1.225 m
1.227 m
1.229 m
Q.23
If the areas of 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 :
10 cm
15 cm
20 cm
30 cm
Q.24
The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is $$301\frac{5}{7}$$ cm
^{3}
, what is its slant height ?
8 cm
9 cm
10 cm
12 cm
Q.25
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. The area of the canvas required for the tent is :
1300 m
^{2}
1310 m
^{2}
1320 m
^{2}
1330 m
^{2}
Q.26
How many cubes of 10 cm edge can put in a cubical box of 1 m edge ?
10
100
1000
10000
Q.27
Two rectangular sheets of paper, each 30 cm × 18 cm are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is :
2 : 1
3 : 2
4 : 3
5 : 3
Q.28
A 4 cm cube is cut into 1 cm cubes. The total surface area of all the small cubes is :
24 cm
^{2}
96 cm
^{2}
384 cm
^{2}
None of these
Q.29
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
12$$\pi$$ cm
^{3}
15$$\pi$$ cm
^{3}
16$$\pi$$ cm
^{3}
20$$\pi$$ cm
^{3}
Q.30
In a right circular cone, the radius of its base is 7 cm and its height is 24 cm. A cross-section is made through the mid-point of the height parallel to the base. The volume of the upper portion is :
154 cm
^{3}
169 cm
^{3}
800 cm
^{3}
1078 cm
^{3}
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