The volume of a cone is 27∏ and the radius is 3. Can you find the length of the height?

My teacher requires work if it is not too much of a hassle please SHOW WORK!!!! thank you for helping.

1 Answer
Mar 7, 2017

The height is #9# units

Explanation:

The volume of the cone is given as #27pi# (unknown) cubic units.
You can make it a big cone that you can walk into and use #m^3#
or a small cone sitting on your table and use #cm^3#

The volume of a cone is: #V = pir^2 (h/3)#

Then: #27pi = pi(3)^2 (h/3)#

#27pi = pi(3)h#

#9pi = pih#

#h = 9# units

If you started with the big cone, the height is #9m# or #30ft#,
and if you decided on the small cone, the height is #9cm # or #3.5# inches.