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 #36 # and the height of the cylinder is #6 #. If the volume of the solid is #48 pi#, what is the area of the base of the cylinder?

Question

1287 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-23T00:56:43

#A=2.667pi#

#A = 8.37#

enter image source here

We can use the volume of the shape to solve for the radius using the combination of the volume of the cylinder and the cone.

Volume of a Cone = #1/3pir^2h#
Volume of a Cylinder = #pir^2h#

Total Volume = #1/3pir^2h+pir^2h#

#48pi = 1/3pir^2(36)+pir^2(6)#

#48pi = 12pir^2+6pir^2#

#48pi = 18pir^2#

#(48cancelpi)/(18cancelpi) = ((cancel18cancelpi)r^2)/(cancel18cancelpi)#

#2.667 = r^2#

#sqrt2.667 = sqrt(r^2)#

#1.633 = r#

Area of the circular base is #A=pir^2#

#A=pi(1.633)^2#

#A=2.667pi#

#A = 8.37#