Page 1 - Home Assignment-4-Ch-13 SA and Volume(Sphere)
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SAI International School
                                                     CLASS - IX

               Mathematics
               CHAPTER-13: SURFACE AREAS AND VOLUMES

               HOME ASSIGNMENT-4 [SPHERE]
               1.    If the surface area and volume of a sphere are numerically equal, then find the
                     radius of the sphere.
               2.    A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled
                     into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many
                     bottles are needed to empty the bowl?
               3.
                     A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular
                     cone of base radius 6 cm. Determine the height of the cone.

               4.
                     Two identical solid hemispheres of equal base radius r cm are stuck together along
                     their bases. What will be the total surface area of combining solid formed?
               5.    If volumes of two spheres are in the ratio 64 : 27, then find the ratio of their surface

                     areas.
               6.    A spherical ball is divided into two equal halves. If the curved surface area of each
                     half is 56.57 cm? Find the volume of the spherical ball. [use π = 3.14]
               7.    A metallic spherical shell of internal and external diameters 4 cm and 8 cm,
                     respectively is melted and recast into the form a cone of base diameter 8 cm. Find
                     the height of the cone.

               8.    The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its
                     volume.
               9.    Twelve solid spheres of the same size are made by melting a solid metallic cylinder
                     of base diameter 2 cm and height 16 cm. What will be the diameter of each
                     sphere?
               10.  How many spherical lead shots each of diameter 4.2 cm can be obtained from a
                     solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm?



               HOME ASSIGNMENT-4  ANSWERS

               1.    r= 3
               2.    54

               3.    28.44 cm

               4.    4πr
                         2
               5.    16 : 9


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