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GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , PRACTICE EXERCISE 13.1, Q.1 Three cubes each of side 5 cm are joined end to end. Find the surface area, of the resulting cuboid., Ans. Surface area of the cuboid = 350 cm, Q.2 A toy is in the form of a cone surmounted on a hemisphere. The diameter, of the base and the height of the cone are 6 cm and 4 cm, respectively., Determine the surface area of the toy. (Use π = 3.14), 2. 103. 62 cm, Q.3 A solid is in the form of a right circular cylinder, with a hemisphere at one, end and a cone at the other end. The radius of the common base is 3.5 cm and, the heights of the cylindrical and conical portions are 10 cm. and 6 cm,, respectively. Find the total surface area of the solid. (Use π = 22 / 7) ,, 3. 372. 56 cm, Q.4 A solid sphere of radius 3 cm is melted and then cast in to small spherical, balls each of diameter 0.6 cm. Find the number of balls thus obtained., Ans. 1000 spherical balls are obtained by melting the given solid sphere., Q.5 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?, Ans. 9979.2 litres of water flows out per hour., Q.6 A conical hole is drilled in a circular cylinder of height 12 cm and base, radius 5 cm. The height and the base radius of the cone are also the same. Find, the whole surface and volume of the remaining cylinder., 6. Volume =200 π cm , Surface area = 210 π cm, Q.7 A cylindrical vessel of diameter 14 cm and height 42 cm is fixed, , GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 1

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GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The, total space between the two vessels is filled with cork dust for heat insulation, purposes. How many cubic centimeters of cork dust will be required?, 7. 1980 cm, Q.8 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., Ans. The width of the embankment is 10.5 m., Q.9 A rocket is in the form of a circular cylinder closed at the lower end with a, cone of the same radius attached to the top. The cylinder is of radius 2.5 m and, height 21 m and the cone has the slant height 8 m. Calculate the total surface, area and the volume of the rocket., 9. 412.5 m , 461.77 cm, Q.10 A right circular cylinder having diameter 12 cm and height 15 cm is full, ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter, 6 cm having a hemispherical shape on the top. Find the number of such cones, which can be filled with ice-cream., 10. 10, Q.11 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 bottoms. Find the, volume of water left in the cylinder, if the radius of the cylinder is 60 cm and, its height is 180 cm., 11. 1.131m, , “Always keep in mind you are unique- just like every body else”, GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 2