The formula for volume of a cone is:
#Vco=pir^2h/3#, where #Vco=#Volume (of cone), #r=#radius, and #h=#height.
Since we know that #h=r#, we can write:
#Vco=pir^3/3#
Substituting the value for the volume:
#36=pir^3/3#
Multiply both sides by #3/pi#.
#36xx3/pi=r^3#
#r^3=108/pi#
The formula for volume of a cylinder is:
#Vcy=pir^2h#, where #Vcy=#Volume (of cylinder), #r=#radius, and #h=#height.
Since we know that #h=r#, we can write:
#Vcy=pir^3#
From the first calculation, we know the value of #r^3# so we substitute that.
#Vcy=pixx108/pi#
#Vcy=cancelpixx108/cancelpi#
#Vcy=108#
Hence, the volume of the cylinder is #108# cubic units.
The formula for volume of a sphere is:
#Vs=4/3pir^3#, where #Vs=#Volume (of sphere), and #r=#radius.
From the first calculation, we know the value of #r^3# so we substitute that.
#Vs=4/3pixx108/pi#
#Vs=4/3cancelpixx108/cancelpi#
#Vs=4/3xx108#
#Vs=4/(1cancel3)xx36cancel108#
#Vs=4xx36#
#Vs=144#
Hence the volume of the sphere is #144# cubic units.
