The formula for the volume of a cone is #V=1/3pir^2h# where
#V# is the volume of the cone
#r# is the radius
#h# is the height
For Cone 1
We have:
#h=6 "in"#
#V=100.38 "in"^3#
#r=?#
And we are trying to find the radius #r#
What we do is substitute what we have into our formula and solve for the unknown (In this case, we solve for #r#)
#100.38=1/3pir^2(6)#
#100.38=6/3pir^2#
#100.38=2pir^2#
#100.38/(2pi)=cancel(2pi)/cancel(2pi)r^2#
#r=+-sqrt((100.38)/(2pi))#
Since #pi=3.14#
#r=sqrt(100.38/(2times3.14)# (Ignore the negative solution)
#r=3.998~~4#
For Cone 2
We have
#d=6 "cm" ->r=d/2=6/2=3"cm"#
#V=56.52"cm"^3#
#h=?#
Again, substitute what we have into our formula and solve for the unknown (In this case, we solve for #h#)
#56.52=1/3pi(3)^2h#
#56.52=3^2/3pih#
#56.52=9/3pih#
#56.52=3pih#
#56.52/(3pi)=cancel(3pi)/cancel(3pi)h#
#56.52/(3times3.14)=h#
#6=h#