# 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 #42 # and the height of the cylinder is #10 #. If the volume of the solid is #144 pi#, what is the area of the base of the cylinder?

QuestionAnswer 1

#V_("cone") = 1/3pir_("cone")^2h_("cone")#

#V_("cylinder") = pir_("cylinder")^2h_("cylinder")#

We have that #r_("cone") = r_("cylinder")# so we shall just denote these as #r#.

#V_("total") = V_("cone") + V_("cylinder") #

#V_("total") = pir^2(1/3h_("cone") + h_("cylinder"))#

#therefore pir^2 = (V_("total"))/(1/3h_("cone") + h_("cylinder"))#

Notice that #pir^2# is precisely the area of the base of the cylinder, which is what we want to calculate so just plug in the numbers:

#A_(base) = (144pi)/(1/3*42 + 10) = (144pi)/(14+10) = (144pi)/(24) = 6pi#

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

HIX Tutor

Solve ANY homework problem with a smart AI

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7