
question_answer1) A cuboidal metal of dimensions \[\text{44 cm}\times \text{3}0\text{ cm}\] \[\times \text{15 cm}\] was melted and cast into a cylinder of height 28 cm. Find its radius.
A) 20cm
B) 15cm
C) 10cm
D) 18cm
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question_answer2) The length of the longest rod which can, be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height.
A) 8cm
B) 10cm
C) 12cm
D) 14cm
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question_answer3) The volume of a cube is numerically equal to its surface area. What is the length of its side?
A) 6 units
B) 8 units
C) 9 units
D) 10 units
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question_answer4) The total surface area of a cylinder is 220 sq cm with height 6.5 cm. Find its volume.
A) \[\text{25}.0\text{25 c}{{\text{m}}^{\text{3}}}\]
B) \[\text{2}.\text{5}0\text{25 c}{{\text{m}}^{\text{3}}}\]
C) \[\text{25}0\text{2}.\text{5 c}{{\text{m}}^{\text{3}}}\]
D) \[\text{25}0.\text{25 c}{{\text{m}}^{\text{3}}}\]
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question_answer5) The lateral surface area of a cylinder is 176 \[\text{c}{{\text{m}}^{\text{2}}}\]and its base area is\[~\text{38}.\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\].What is its volume?
A) \[\text{83}0\text{ c}{{\text{m}}^{\text{3}}}\]
B) \[\text{38}0\text{ c}{{\text{m}}^{\text{3}}}\]
C) \[\text{3}0\text{8 c}{{\text{m}}^{\text{3}}}\]
D) \[\text{8}0\text{3 c}{{\text{m}}^{\text{3}}}\]
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question_answer6) Identify the ratio of lateral surface areas of two cylinders with equal heights.
A) H: h
B) R: r
C) 1: 2
D) 2:3
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question_answer7) A cone and a hemisphere have equal bases and equal volumes. Identify the ratio of their heights.
A) 1 : 3
B) 1 : 2
C) 2 : 1
D) 3 : 1
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question_answer8) The area of the base of a cone is 616 sq cm. Its height is 48 cm. Find its total surface area.
A) \[\text{2816}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{2861 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{2618}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{2681 c}{{\text{m}}^{\text{2}}}\]
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question_answer9) From a circle of radius 15 cm, a sector central angle\[~\text{216}{}^\circ \]is cut and its bounding radii are joined without overlap so as to form a cone. Find its volume.
A) \[\text{1}0\text{81}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\]
B) \[\text{1}0\text{71}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\]
C) \[\text{1}0\text{18}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[~\text{1}0\text{61}.\text{9}\,\text{c}{{\text{m}}^{\text{3}}}\]
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question_answer10) A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, what is the rise in the level of water?
A) 0.8 cm
B) 0.5 cm
C) 0.1 cm
D) 0.3 cm
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question_answer11) The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. What is the length of the wire?
A) 36 cm
B) 360 cm
C) 3600 cm
D) 306 cm
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question_answer12) A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The raise in water level is 0.8 cm. Find the diameter of each ball.
A) 0.8 cm
B) 0.4 cm
C) 0.2 cm
D) 0.6 cm
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question_answer13) Three solid glass balls of radii 'r' cm, 6 cm and 8 cm are melted into a solid sphere of radius 9 cm. Find the value of 'r'.
A) \[\frac{1}{4}cm\]
B) \[\frac{1}{3}cm\]
C) \[\frac{1}{2}cm\]
D) 1 cm
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question_answer14) A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. What is the volume of steel used?
A) \[\text{42}.\text{15 c}{{\text{m}}^{\text{3}}}\]
B) \[~\text{41}.\text{52 c}{{\text{m}}^{\text{3}}}\]
C) \[\text{41}.\text{25}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{43}.\text{21c}{{\text{m}}^{\text{3}}}\]
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question_answer15) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
A) 14cm
B) 12cm
C) 16cm
D) 18cm
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question_answer16) A circus tent is in the form of a cone over a cylinder. The diameter of the base is 9 m, the height of cylindrical part is 4.8 m and the total height of the tent is 10.8m. What area of canvas is required for the tent?
A) 24.184 sq. m
B) 2418.4 sq. m
C) 241.84sq.m
D) 24.164 sq. m
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question_answer17) If the radii of the circular ends of a conical bucket of height 45 cm are 28 cm and 7 cm, what is the capacity of the bucket?
A) \[\text{4815}0\,\text{c}{{\text{m}}^{\text{3}}}\]
B) \[\text{4851}0\,\text{c}{{\text{m}}^{\text{3}}}\]
C) \[\text{48105}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{48}0\text{15}\,\text{c}{{\text{m}}^{\text{3}}}\]
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question_answer18) 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 is\[\frac{1}{27}\]. the volume of cone, what is the height at which the section is made?
A) 10 cm
B) 15 cm
C) 20 cm
D) 19 cm
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question_answer19) A top is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3.5 cm. The total height of the top is 15.5 cm. Find the total area of the top.
A) \[\text{214}.\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{21}.\text{45}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[~\text{215}.\text{4}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{21}.\text{43}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer20) The base radius of a cylinder is\[1\frac{2}{3}\]. times its height. The cost of painting its curved surface area at \[\text{2 paise}/\text{c}{{\text{m}}^{\text{2}}}\]is ` 92.40. Find the volume of the liquid.
A) \[\text{8}0\text{85}0\text{ c}{{\text{m}}^{\text{3}}}\]
B) \[\text{8}0\text{58}0\text{ c}{{\text{m}}^{\text{3}}}\]
C) \[\text{8}0\text{5}0\text{8 c}{{\text{m}}^{\text{3}}}\]
D) \[\text{8}00\text{5}0\text{8 c}{{\text{m}}^{\text{3}}}\]
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question_answer21) A cylindrical vessel contains 49.896 litres of liquid. The cost of painting its curved surface area at 2 paise/sq cm is ` 95.04. Find its total surface area.
A) \[\text{5724 c}{{\text{m}}^{\text{2}}}\]
B) \[~\text{7524 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{5742 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{7254 c}{{\text{m}}^{\text{2}}}\]
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question_answer22) The ratio of base radius and height of a cone is 3 :4. If the cost of smoothening the curved surface area at 5 paise/sq cm is ` 115.50, find the volume of cone.
A) \[\text{12963}\,\text{c}{{\text{m}}^{\text{3}}}\]
B) \[\text{12693}\,\text{c}{{\text{m}}^{\text{3}}}\]
C) \[\text{12936}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{12639}\,\text{c}{{\text{m}}^{\text{3}}}\]
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question_answer23) A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, find the cost of repairing its curved surface area at? 12/sq m.
A) ` 5.94
B) ` 6.94
C) ` 7.95
D) ` 9.65
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question_answer24) The cost of painting the curved surface area of a cone at \[\text{5 ps}/\text{c}{{\text{m}}^{\text{2}}}\]is ` 35.20, find the volume of the cone if its slant height is 25 cm.
A) \[\text{1223}\,\text{c}{{\text{m}}^{\text{3}}}\]
B) \[\text{1232}\,\text{c}{{\text{m}}^{\text{3}}}\]
C) \[~\text{1323}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{1332}\,\text{c}{{\text{m}}^{\text{3}}}\]
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question_answer25) A piece of metal pipe is 77 cm long with inside diameter of the cross section as 4 cm. If the outer diameter is 4.5 cm and the metal weighs 8 gm/cu cm, find the weight of pipe.
A) 2.057 kg
B) 20.57 kg
C) 205.7 kg
D) 2.097 kg
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question_answer26) A rectangular solid metallic cuboid \[\text{9 cm}\times \text{8 cm }\times \text{2 cm}\] is melted and recast into solid cubes each of side 2 cm. How many such solid cubes can be made?
A) 20
B) 18
C) 12
D) 15
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question_answer27) The side of a solid metallic cube is 50 cm. It is melted and recast into 8000 similar solid cubical dice. Find the side of each die.
A) 2.5 cm
B) 6 cm
C) 1.9cm
D) 5.2cm
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question_answer28) Water flows at the rate of 5 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 25 m long and 22 m wide. Find the time in which the level of water in the tank rises by 21 cm. [Take\[\pi =\frac{22}{7}\].]
A) 2 hours
B) 5 hours
C) 3 hours
D) 1.5 hours
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question_answer29) Two right circular cones X and Y are made such that X has a radius three times the radius of Y and Y has a volume half the volume of X. What is the ratio of heights of X and Y?
A) 5:8
B) 4:7
C) 2:9
D) 3:5
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question_answer30) Rain water from a roof \[\text{22 m }\times \text{ 2}0\text{ m}\] drains into a cylindrical vessel with diameter of base 2 m and height 3.5 m. If the vessel is just full, find the amount of rainfall in cm.
A) 4.5 cm
B) 2.5 cm
C) 3 cm
D) 1 cm
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question_answer31) The diameter of a solid metallic sphere is 16 cm. The sphere is melted and recast into 8 similar solid spherical balls. What is the radius of the each of the balls?
A) 2 cm
B) 3 cm
C) 4 cm
D) 6 cm
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question_answer32) A hemispherical bowl of internal diameter 36 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?
A) 24
B) 35
C) 12
D) 48
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question_answer33) If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
A) 1 :4
B) 2:3
C) 1:2
D) 5:7
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question_answer34) 56 circular plates, each of radius 5 cm and thickness 0.25 cm, are placed one above the other to form a solid right circular cylinder. Find the volume of the cylinder so formed.
A) \[\text{9}00\text{ c}{{\text{m}}^{\text{3}}}\]
B) \[\text{885 c}{{\text{m}}^{\text{3}}}\]
C) \[~\text{11}00\text{ c}{{\text{m}}^{\text{3}}}\]
D) \[~\text{125}0\,\text{c}{{\text{m}}^{\text{3}}}\]
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question_answer35) A semicircular piece of paper of radius 14 cm is rolled to form a cone of the largest possible size. Find the capacity of the cone.
A) \[\text{721}.\text{5c}{{\text{m}}^{\text{3}}}\]
B) \[\text{645}.\text{1}0\text{c}{{\text{m}}^{\text{3}}}\]
C) \[\text{449}.\text{64 c}{{\text{m}}^{\text{3}}}\]
D) \[\text{622}.\text{37 c}{{\text{m}}^{\text{3}}}\]
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question_answer36) In a solid cylinder of height 10 cm and diameter 8 cm, two equal conical cavities have been made at both its ends. If the diameter of the cavity is 6 cm and height 4 cm, find the volume of the remaining solid in terms of\[\pi \].
A) \[\text{95}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]
B) \[\text{136}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]
C) \[\text{216}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]
D) \[\text{192}\,\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]
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question_answer37) A solid sphere and a solid hemisphere have the same total surface area. Find the ratio of their volumes.
A) \[\sqrt{3}:1\]
B) \[3\sqrt{3}:5\]
C) \[3\sqrt{3}:4\]
D) \[1:\sqrt{3}\]
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question_answer38) A sphere, of diameter 12 cm, is dropped into a right circular cylindrical vessel, partly filled with water. If the sphere is completely immersed in water, the water level in the cylindrical vessel rises by\[3\frac{5}{9}\]cm. Find the diameter of the cylindrical vessel.
A) 16cm
B) 18cm
C) 12cm
D) 13cm
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question_answer39) The largest right circular cone is carved out of a cube whose edge is of length 'p' units. Find the volume of the cone.
A) \[\frac{\pi {{p}^{3}}}{12}cu.units\]
B) \[\frac{\pi {{p}^{3}}}{4}cu.units\]
C) \[\pi {{p}^{3}}cu.units\]
D) \[\frac{\pi {{p}^{3}}}{5}cu.units\]
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question_answer40) A rightangled triangle ABC, where\[\angle B={{90}^{o}}\], is rotated about BC. If BC = 16 cm and AC = 20 cm, find the volume of the right circular cone traced out by the triangle.
A) \[\text{2413}\,\text{c}{{\text{m}}^{\text{3}}}\]
B) \[\text{2311 c}{{\text{m}}^{\text{3}}}\]
C) \[\text{1254}\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{1725c}{{\text{m}}^{\text{3}}}\]
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question_answer41) A bucket of height 16 cm made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15 cm respectively. What is the slant height of the bucket?
A) 15cm
B) 20cm
C) 5cm
D) 12cm
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question_answer42) A rightangled triangular plate of smaller sides measuring 5 cm and 12 cm is rotated about the longest side to trace a double cone as shown in the figure. Find the ratio of the curved surface areas of the two cones.
A) 6:1
B) 5:12
C) 3:14
D) 6:5
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question_answer43) The largest possible cube is made from a wooden sphere of radius \[6\sqrt{3}\,cm\]cm. Find the surface area of the cube.
A) \[\text{864}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{542}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[\text{735}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{625}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer44) The radii of circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
A) \[\text{1564}.\text{15}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{7599}.\text{43}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[\text{6542}.\text{1 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{8265}.\text{14}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer45) The ratio of the radii of two spheres is 3 :2. Find the ratio of their volumes.
A) 25:4
B) 5:16
C) 9:14
D) 27:8
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question_answer46) A cylindrical can whose base is horizontal and of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed in the can, water just covers the sphere. Given that the sphere just fits in the can, find the depth of water in the can before the sphere was put into it.
A) 2.3 cm
B) 5.1 cm
C) 1.5cm
D) 3.2cm
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question_answer47) The internal and external radii of a hemispherical metallic vessel are 7 cm and 10.5 cm respectively. If \[\text{1 c}{{\text{m}}^{\text{3}}}\]of the metal weighs 10 g, find the weight of the vessel.
A) 25.15kg
B) 32.1 kg
C) 17.07kg
D) 16.27kg
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question_answer48) A tent is made in the form of a frustrum A of a right circular cone surmounted by another right circular cone B. The diameter of the ends of the frustrum A are 8 m and 4 m, its height is 3 m and the height of the cone B is 2 m. What is the area of the canvas required for the tent?
A) \[\text{86}.\text{75 }{{\text{m}}^{\text{2}}}\]
B) \[\text{85}.\text{77 }{{\text{m}}^{\text{2}}}\]
C) \[\text{86}.\text{77 }{{\text{m}}^{\text{2}}}\]
D) \[\text{87}.\text{67 }{{\text{m}}^{\text{2}}}\]
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question_answer49) What is the maximum distance between any two points of a cube of side T units?
A) \[(\sqrt{2}+1)l\,units\]
B) \[\sqrt{2}\,l\,units\]
C) \[\sqrt{3}\,l\,units\]
D) \[2\,l\,units\]
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