Page 1 - Worksheet-4- Sa & V [Sphere]
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SAI International School
                                                     CLASS - IX

               Mathematics
               CHAPTER-13: SURFACE AREAS AND VOLUMES

                Worksheet -4 [SPHERE]
               1.    The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is            1
                     being pumped into it. The ratios of the surface areas of the balloon in the two
                     cases is
                     a. 1: 4       b. 1: 3        c. 2: 3        d. 2: 1
               2.    The radii of two cylinders are in the ratio of 2: 3 and their heights are in the ratio   1
                     of 5: 3. The ratio of their volumes is
                     a. 10:17    b.  20:27    c. 17:27      d. 20:37

               3.    The volume of the largest right circular cone that can be fitted in a cube whose        1
                     edge is 2r equals to the volume of a hemisphere radius r. True/False. Justify.
               4.    The volume of a sphere is equal to two-third of the volume of a cylinder whose          1
                     height and diameter are equal to the diameter of the sphere. State True/False.
               5.    If the radius of a sphere is 2r, then its volume will be                                1




               6.    A metallic spherical shell of internal and external diameters 4 cm and 8 cm,            1
                     respectively is melted and recast into the form a cone of base diameter 8 cm.
                     The height of the cone is
                     (a) 12 cm                (b) 14 cm             (c) 15 cm                   (d) 18 cm
               7.    Twelve  solid  spheres  of  the  same  size  are  made  by  melting  a  solid  metallic  1
                     cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere
                     is
                     (a) 4 cm                      (b) 3 cm                     (c) 2 cm                     (d) 6 cm
               8.    If two solid hemispheres of same base radius ‘r’ are joined together along their        1
                     bases, then curved surface area of this new solid is________.
               9.    If volumes of two spheres are in the ratio 64: 27, then the ratio of their surface      1
                     areas is_____.
               10.  A shopkeeper has one spherical ladoo of radius 5 cm. With the same amount of             1
                     material, how many laddoos of radius 2.5 cm can be made?
               11.  A cone, a hemisphere and a cylinder stand on equal bases and have the same               2
                     height. Show that the ratio of their volumes is 1 : 2 : 3.
               12.  A cube of side 4 cm contains a sphere touching its sides. Find the volume of the         2
                     gap in between.
               13.    The volumes of the two spheres are in the ratio 64: 27. Find the ratio of their        2
                      surface areas.

               14.  The water for a factory is stored in a hemispherical tank whose internal diameter        3
                     is 14 m. The tank contains 50 kl of water. Water is pumped into the tank to fill to
                     its capacity. Calculate the volume of water pumped into the tank.


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