Question

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is `27` and the height of the cylinder is `36`. If the volume of the solid is `420 pi`, what is the area of the base of the cylinder?

Answer 1

Volume of solid `V = Axxh_(cy)+1/3xxAxxh_(co)`
Where
Area of cylnder = area of cone = A
Height of cylinder =`h_(cy)=36`
Height of cone =`h_(co)=27`
Volume of the solid`V=420pi`
`:. 18pi= Axx36+1/cancel3xxAxxcancel27^9=45A`
`:. A= (420pi)/45=28/3pi`