posted by Jamie .
Solve for s: h=(square root of 3)times s/2
solve for h
V= (pi)r squared h / 3
Solve for s:
h=(square root of 3)times s/2
Multiply both sides by 2.
2h = (sqrt 3)*s*2/2 which cancels the 2 on the right.
2h = (sqrt 3)*s
Now divide the right side by everything except what you want to keep; in this case, divide by (sqrt 3).
2h/(sqrt 3) = (sqrt 3)*s/(sqrt 3) which eliminates the (sqrt 3) on the right leaving just s.
2h/(sqrt 3) = s.
The second problem will be done the same way. Try your hand and we shall be happy to check your work. Just remember that you must do the same operation to both sides. I hope this helps. A note here:
Some teachers "will not allow" us to keep a sqrt sign in the denominator. If your teacher is one of those, you eliminate the sqrt sign by multiplying both sides by (sqrt 3)/(sqrt 3) [which of course is simply 1/1] or
2h*(sqrt 3)/(sqrt 3*sqrt 3)= s and
2h*(sqrt 3)/3 = s.