A cone is half full of water by volume. how deep is the water in the cone? it has 16cm in height and 12cm in diameter

Question

4745 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-03T14:52:52

#96pi# #"cm"^3# or #301.6# #"cm"^3#

First figure out the total volume, and then figure out how much there is for half of the volume, since the cone is only half full.

The volume of a cone has this formula:

#"volume" = 1/3pir^2h#

#"r = radius"#
#"h = height"#

They gave the diameter, and since the radius is half the diameter, divide it in half:

#r = d/2#

#r = 12/2#

#r = 6#

The radius is #6# and the height is #16#. So we can plug those in and solve:

#"volume" = 1/3pir^2h#

#v = 1/3pi(6)^2(16)#

#v = 1/3pi (36)(16)#

#v = 1/3pi(576)#

#v = 576/3pi#

#v = 192pi#

They want half the volume, so divide #192# by #2# and keep it multiplied by #pi#:

#192/2pi#

#96pi# #"cm"^3#

If it needs to be simplified beyond the terms of #pi#, use your calculator to multiply #96# and #pi#:

#96pi = 301.6# #"cm"^3#