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question_answer1)
A hemispherical bowl is made of steel of \[0.25\text{ }cm\]thickness. The inner radius of the bowl is 5 cm. The volume of steel used is ___. (Use\[\pi =3.141\])
A)
\[42.15\,c{{m}^{3}}\] done
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B)
\[41.52\,c{{m}^{3}}\] done
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C)
\[41.25\,c{{m}^{3}}\] done
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D)
\[40\,c{{m}^{3}}\] done
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question_answer2)
An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use\[\pi =22/7\]]
A)
\[402.12\,c{{m}^{2}}\] done
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B)
\[298\,c{{m}^{2}}\] done
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C)
\[377.14\,c{{m}^{2}}\] done
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D)
\[315\,c{{m}^{2}}\] done
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question_answer3)
A sector of a circle of radius 12 cm has the angle \[{{120}^{\text{o}}}\]. It is rolled up so that two bounding radii are joined together to form a cone. Find the volume of the cone.
A)
\[189.61\text{ }c{{m}^{3}}\] done
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B)
\[169.51\text{ }c{{m}^{3}}\] done
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C)
\[179.61\text{ }c{{m}^{3}}\] done
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D)
\[125.51\text{ }c{{m}^{3}}\] done
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question_answer4)
If the radii of the circular ends of bucket in the form of frustum are 28 cm and 7 cm and the height is 45 cm. The capacity of the bucket is ___.
A)
\[48150\,c{{m}^{3}}\] done
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B)
\[48510\,c{{m}^{3}}\] done
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C)
\[48105\,c{{m}^{3}}\] done
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D)
\[48205\,c{{m}^{3}}\] done
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question_answer5)
The ratio between the volume of two sphere is\[8:27\] what is the ratio between their surface areas?
A)
\[2:3\] done
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B)
\[4:5\] done
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C)
\[5:6\] done
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D)
\[4:7\] done
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question_answer6)
A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
A)
4 cm done
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B)
5 cm done
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C)
3 cm done
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D)
6 cm done
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question_answer7)
A right circular cone is \[4.1\text{ }cm\]high and the radius of its base is \[2.1\text{ }cm\]. Another right circular cone is \[4.3\text{ }cm\]high and the radius of the base is\[2.1\text{ }cm\]. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.
A)
\[6.4\,cm\] done
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B)
\[4.2\,cm\] done
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C)
\[2.1\text{ }cm\] done
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D)
\[5.6\text{ }cm\] done
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question_answer8)
The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is __.
A)
3 done
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B)
4 done
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C)
5 done
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D)
6 done
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question_answer9)
A box opened at the top has its outer dimensions \[10\text{ }cm\text{ }\times 9\text{ }cm\text{ }\times \text{ }2.5\text{ }cm\]and its thickness is \[0.5\text{ }cm,\] find the volume of the metal.
A)
\[92.5\,c{{m}^{3}}\] done
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B)
\[72\,c{{m}^{3}}\] done
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C)
\[63.5\text{ }c{{m}^{3}}\] done
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D)
\[81\text{ }c{{m}^{3}}\] done
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question_answer10)
The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?
A)
20 cm done
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B)
25 cm done
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C)
10 cm done
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D)
15 cm done
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question_answer11)
A cuboidal metal of dimensions \[44\text{ }cm\times 30\text{ }cm\times 15\text{ }cm\]was melted and cast into a cylinder of height 28 cm. Its radius is
A)
20cm done
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B)
15cm done
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C)
10cm done
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D)
25cm done
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question_answer12)
Study the question and the statements given below and decide which of the statements) is/are necessary to answer the question. What is the capacity of the cylindrical tank?
I. The area of the base is 61,600 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 done
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B)
Only II and III done
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C)
Only I and Ill done
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D)
Only II and either I or III done
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question_answer13)
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the for of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is \[3.5\text{ }cm\]and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take\[\pi =22/7\])
A)
\[616\,c{{m}^{3}}\] done
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B)
\[600\,\,c{{m}^{3}}\] done
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C)
\[535\,\,c{{m}^{3}}\] done
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D)
\[716\,c{{m}^{3}}\] done
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question_answer14)
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.
A)
\[\frac{4}{3}\,\pi {{r}^{3}}\,\] done
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B)
\[2\,\pi {{r}^{3}}\,\] done
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C)
\[\frac{1}{3}\,\pi {{r}^{3}}\,\] done
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D)
\[\frac{2}{3}\,\pi {{r}^{3}}\,\] done
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question_answer15)
A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is\[0.8\,cm.\]. The diameter of each ball is __.
A)
\[0.8\text{ }cm\] done
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B)
\[0.4\text{ }cm\] done
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C)
\[0.2\text{ }cm\] done
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D)
\[0.5\text{ }cm\] done
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question_answer16)
A tent is in the shape of a right circular cylinder up to a height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of \[Rs.\text{ }2\text{ }per\text{ }{{m}^{2}},\]if the radius of the base is 14 m.
A)
Rs.2068 done
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B)
Rs.2156 done
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C)
Rs.2248 done
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D)
Rs.1872 done
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question_answer17)
The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint \[1\text{ }c{{m}^{2}}\]of the surface is\[Rs.\text{ }0.05\].Find the total cost to painting the vessel all over.
A)
Rs.108.32 done
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B)
Rs.296.28 done
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C)
Rs.101.59 done
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D)
Rs. 96.28 done
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question_answer18)
A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many litres can the bucket hold?
A)
\[13\,L\] done
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B)
\[27\text{ }L\] done
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C)
\[42.94\text{ }L\] done
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D)
\[28.49\text{ }L\] done
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question_answer19)
To construct a wall 24 m long, \[0.4\text{ }m\]thick and 6 m high, bricks of diamensions \[25\text{ }cm\text{ }\times 16\text{ }cm\text{ }\times \text{ }10\text{ }cm\]each are used. If the mortar occupies 1/10th of the volume of the wall, find the number of bricks used.
A)
12960 done
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B)
14420 done
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C)
24566 done
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D)
14296 done
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question_answer20)
In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person have 4 sq. metres of the space on ground and 20 cubic metres of air to breath. What should be the height of the conical tent?
A)
20m done
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B)
15m done
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C)
12m done
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D)
30m done
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question_answer21)
A conical vessel of radius 12 cm and height 16 cm is completely filled with water. A sphere is lowered into the water and its sized is such that, when it touches the sides, it is just immersed. What fraction of the water overflows?
A)
\[\frac{3}{8}\] done
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B)
\[\frac{4}{7}\] done
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C)
\[\frac{1}{2}\] done
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D)
\[\frac{5}{9}\] done
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question_answer22)
The decorative block shown in the figure is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of\[4.2\text{ }cm\]. The total surface area of the block is __.
A)
\[150\,\,c{{m}^{2}}\] done
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B)
\[160.86\,c{{m}^{2}}\] done
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C)
\[162.86\,c{{m}^{2}}\] done
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D)
\[163.86\,c{{m}^{2}}\] done
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question_answer23)
Which of the following statement is INCORRECT?
A)
If from a solid cubic block a hemi-sphere of maximum diameter is cut-off then surface area of the cubic block is decrease. done
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B)
If two sphere are melted to form a cylinder then surface area of cylinder is the sum of surface area of two sphere. done
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C)
if a wire is wound about a cylinder so as to cover the whole surface, then length of the wire is equal to the surface area of the cylinder. done
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D)
All of these. done
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question_answer24)
A tent is made in the form of a frustum of a cone surmounted by another cone. The diameter of the base and the top of the frustum are 20 m and 6 m respectively and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required.
A)
\[924.71\text{ }{{m}^{2}}\] done
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B)
\[1402.23\text{ }{{m}^{2}}\] done
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C)
\[1124.56\,{{m}^{2}}\] done
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D)
\[1068.57\,{{m}^{2}}\] done
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question_answer25)
The interior of a building is in the form of cylinder of diameter \[4.3\text{ }m\]and height 3.8 m, surmounted by a cone whose vertical angle is a right angle. Find the volume and curved surface area of the building respectively. (Take\[\pi =3.14\]).
A)
\[65.56\text{ }{{m}^{3}},\text{ }71.83\text{ }{{m}^{2}}\] done
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B)
\[70.24\text{ }{{m}^{3}},\text{ }62.24\text{ }{{m}^{2}}\] done
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C)
\[62.26\text{ }{{m}^{3}},\text{ }75.56\text{ }{{m}^{2}}\] done
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D)
\[72.26\text{ }{{m}^{3}},\text{ }66.46\text{ }{{m}^{2}}\] done
clear
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