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According to question, small spheres are melted and converted into a bigger sphere. Thus the sum of their volume is equal to the volume of the bigger sphere.   The volume of 3 small spheres =  Volume of bigger sphere Let us assume the radius of the bigger sphere is r. Hence the radius of the sphere obtained is 12 cm.
Let us assume the height of the cylinder to be h. Since the material is melted and recast thus its volume will remain the same. So, Volume of sphere =  Volume of obtained cylinder.                                                                                     Hence the height of the cylinder is 2.74 cm.
The volume of the vessel is given by :  Volume of vessel  =  Volume of sphere  +  Volume of the cylindrical part  Now, the volume of the sphere is  :                         And the volume of the cylinder is:-                                Thus the volume of the vessel is
It is clear from the question that the required volume is :                                 The volume of water (left)    =Volume of a cylinder - Volume of solid Now the volume of the cylinder is     or                                                  And the volume of solid is :                                                                    Thus the volume of water left :                ...
The pole can be divided into one large cylinder and one small cylinder. Thus, volume of pole  =  volume of large cylinder   +     volume of small cylinder                                     or                                 or                                 or                                 or                                 Now, according to question mass of the pole is :                  ...
According to the question :  Water spilled from the container  =   Volume of lead balls. Let us assume the number of lead balls to be n. Thus the equation becomes :                                     or                               or                                           or                                            Hence the number of lead shots dropped are 100.
The volume of wood is given by = volume of the cuboid - the volume of four cones. Firstly, the volume of cuboid :     or                                          or                                          And, the volume of cone :                                                                      Thus the volume of wood is
It is clear from the figure that gulab jamun has one cylindrical part and two hemispherical parts. Thus, the volume of gulab jamun is   =   Volume of cylindrical part  +  2 (Volume of the hemisphere ) Now, the volume of the cylinder is  or                                          or                                          And the volume of a hemisphere is  :                                  ...
The volume of air present  =   Volume of cylinder   +   2 (Volume of a cone) Now, the volume of a cylinder :     or                                          or                                          And the volume of a cone is :                                               or                                           or                                           Thus the volume of air is :  ...
The volume of the solid is given by : The volume of solid  =   Volume of cone   +   Volume of a hemisphere The volume of cone    :                                           or                                      or                                      And the volume of the hemisphere :                                              or                                         or                   ...
Firstly we need to calculate the slant height of cone :                                                        or                                                          or                                                    or                                                    Now, the total surface area of solid can be calculated as : The surface area of solid   =   Surface area of cylinder ...
The canvas will cover the cylindrical part as well as the conical part. So,     the area of canvas   =   Area of cylindrical part (curved)   +   Area of the conical part Now, the area of the cylindrical part is   or                                                       or                                                       And the area of the cone is    or                                 ...
It is clear from the figure that the capsule has hemisphere and cylinder structure.   The surface area of capsule  =   2 (Area of the hemisphere)   +   Area of the cylindrical part Area of hemisphere   or                               or                               And the area of the cylinder    or                                or                               Thus the area of the solid is ...
It is given that the diameter of the hemisphere is equal to the edge length of the cube.  The total surface area of solid is given by : The surface area of solid   =   Surface area of cube   +   Surface area of the hemisphere  -  Area of the base of the hemisphere The surface area of the cube    And surface area of the hemisphere:   Area of base of the hemisphere:   Thus the area of solid is:
It is given that hemisphere is mounted on the cuboid, thus the hemisphere can take on complete as its diameter (which is maximum). Thus the greatest diameter of the hemisphere is 7 cm. Now, the total surface area of solid  =   Surface area of cube  +   Surface area of the hemisphere -  Area of the base of a hemisphere (as this is counted on one side of the cube) The surface area of the cube is...
The required surface area of the toy is given by :  Area of toy  =   Surface area of hemisphere   +   Surface area of the cone Firstly consider the hemisphere :   The surface area of a hemisphere is    or                                                or                                                 Now for cone we have :                                  The surface area of a cone   Thus...
Since the vessel consists of hemisphere and cylinder, thus its area is given by :                         Area of vessel   =  Inner area of the cylinder(curved)  +  Inner area of hemisphere The inner surface area of the hemisphere is :                                                  or                                             or                                            And the surface...
We are given that volume of the cube   Also, the volume of cube is given by      ( here    is the edge of the cube) Thus :                                                                                            Now according to the question we have combined the two cubes that edge lengths of the formed cuboid are 4 cm, 4 cm and 8 cm. The surface area of a cuboid is :      or             ...
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