7.  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 of the cylinder is 60 cm and its height is 180 cm.

Answers (1)

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   =\ \pi r^2h

 or                                                  =\ \pi\times (60)^2\times 180\ cm^3

And the volume of solid is :

                                            \\=\ \frac{1}{3} \pi r^2h\ +\ \frac{2}{3}\pi r^3\\\\=\ \frac{1}{3} \times \pi \times (60)^2\times 120\ +\ \frac{2}{3}\times \pi \times (60)^3\\\\=\ \pi (60)^2\times 80\ cm^3                      

Thus the volume of water left :

                                              \\=\ \pi (60)^2\times 180\ -\ \pi (60)^2\times 80\\\\=\ \pi (60)^2\times 100\\\\=\ 1131428.57\ cm^3\\\\=\ 1.131\ m^3                                                               

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