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M.K. MATHEMATICS (M.:-8826181724), , CLASS:-X, , GALACTIC INSTITUTE, MATHEMATICS TEST, TIME: 1.15hrs., , CHAPTER-13, , [M.M.: 30], , Very Short Answer Questions, (1 mark), Q.1 The volumes of two spheres are in the ratio 64:27. The ratio of their, surface areas is, (a) 1:2, (b)2:3, (c) 9:16, (d) 16: 9, Q.2 A solid sphere of radius r is melted and cast into the shape of a solid cone, of height r, the radius of the base of the cone is, (a) 2r, (b) 3r, (c) r, (d) 4r, Long Answer Question, (2 marks), Q.3 Three cubes each of side 5 cm are joined end to end. Find the surface area, of the resulting cuboid., Long Answer Question, (3 marks), Q.4 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? (1000𝑐𝑚 = 1𝑙), Q.5 A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its, top, which is open, is 5 cm. It is filled with water upto the brim. When lead shots,, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one fourth of, the water flows out. Find the number of lead shots dropped in the vessel., Q.6 A wooden article was made by scooping out a hemisphere from each end, of a solid cylinder, as shown in Fig. 16.37. If the height of the cylinder is 10 cm,, and its base is of radius 3.5 cm, find the total surface area of the article., , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 1

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M.K. MATHEMATICS (M.:-8826181724), , CLASS:-X, , Long Answer Question, (4 marks), Q.7 A well, whose diameter is 7m, has been dug 22.5 m deep and the earth, dugout is used to form an embankment around it If the height of the, embankment is 1.5 m, find the width of the embankment., Q.8 A solid consisting of a right circular cone of height 120 cm and radius 60 cm, standing on a hemisphere of radius 60 cm is placed upright in a right circular, cylinder full of water such that it touches the bottom. Find the volume of water left, in the cylinder, if the radius is 60 cm and its height is 180 cm., Q.9 A tent is in the shape of a cylinder surmounted by a conical top. If the height, and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant, height of the top is 2.8 m, find the area of the canvas used for making the tent. Also,, find the cost of the canvas of the tent at the rate of Rs 500 per m2. (Note that the, base of the tent will not be covered with canvas.) (Use π=722)., , “Education is the movement from darkness to light”, ALL THE BEST, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 2