Question #d236c

1 Answer
Oct 6, 2017

For Cone 1
Radius #=4"in"#

For Cone 2
Height # = 6"cm"#

Explanation:

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#