Question

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 up right 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 cylinder is 60 cm and its height is 180 cm

Answer 1

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Answer 2

Answer:

Volume of Water left in Cylinder = 1131428.57 cm³

Step-by-step explanation:

Given: Height of Cone, h = 120 cm and Radius of Cone, r = 60 cm

           Radius of Hemisphere, r = 60 cm

          Height of Cylinder, H = 180 cm and Radius of Cylinder, r = 60 cm

To find: Volume of water left in cylinder

Volume of water left in cylinder = volume of cylinder - ( volume

                                                 of cone + volume of hemisphere )

                                                    = $\pi r^2H-(\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3)$

                                                    = $\pi r^2(H-(\frac{1}{3}h+\frac{2}{3}r))$

                                                    = $\frac{22}{7}\times60^2(180-(\frac{1}{3}\times120+\frac{2}{3}\times60))$

                                                    = $\frac{22}{7}\times3600(180-(40+40))$

                                                    = $\frac{22}{7}\times3600\times100$

                                                    = 1131428.57 cm³

Therefore, Volume of Water left in Cylinder = 1131428.57 cm³