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 #9 # and the height of the cylinder is #12 #. If the volume of the solid is #48 pi#, what is the area of the base of the cylinder?

1 Answer
A08
Apr 15, 2016

#3.2pi#

Explanation:

Volume of a right circular cone is given by the expression
#V_"cone"=pir^2h/3#, where #pir^2# is the area of the base and #h# is the vertical height.
Also that Volume of a cylinder #V_"cylinder"=pir^2h#, where #pir^2# is the area of the base and #h# is cylinder's height.

Volume of the given solid #=V_"cone"+V_"cylinder"#
#=1/3"area of the base of cone"xx"height of cone"+"area of the base"xx"height of cylinder"#
Inserting given values

#48pi=1/3"area of the base of cone"xx9+"area of the base of cylinder"xx12#

Since, radius of both cone and cylinder are equal, rearranging and solving for area of the base of cylinder
#15xx"area of the base of cylinder"=48pi#
#"Area of the base of cylinder"=cancel48^16/cancel15_5pi#
#=3.2pi#

Related questions
See all questions in Volume of Solids
Impact of this question
1610 views around the world
You can reuse this answer
Creative Commons License