Find a function that models surface area of a cylinder in terms of its height . The volume of a cylinder is 300 cm^3 .
I know the volume of a cylinder is v= 3.14•r^2•h and Surface area is 2•3.14•r^2+2 •3.14•r•h. I found that r^2 = 300\ 3.14h what do I do from there?
You got r = √(300/πh)
Thus, the area is
2πr^2 + 2πrh = 2πr(r+h) = 2π√(300/πh)(√(300/πh)+h)
Well, first of all, let's correct a small mistake. The volume of a cylinder should be given by π • r^2 • h, not 3.14 • r^2 • h. So the correct equation would be V = π • r^2 • h.
Now, to find a function that models the surface area of a cylinder in terms of its height, we need to use the correct formula for surface area, which is A = 2π • r^2 + 2π • r • h.
Since we know the volume of the cylinder is 300 cm^3, we can substitute this value into the volume equation to get:
300 = π • r^2 • h
Now, let's solve this equation for r^2 to get it in terms of h:
r^2 = 300 / (π • h)
Next, substitute this value for r^2 into the surface area formula:
A = 2π • (300 / (π • h)) + 2π • r • h
Simplifying this equation gives us the function that models the surface area of the cylinder in terms of its height:
A = 600/h + 2π • r • h
This is the equation you were looking for!
To find a function that models the surface area of a cylinder in terms of its height, you can substitute the expression for r^2 into the surface area formula.
Given that r^2 = 300 / (3.14h), you can replace r^2 in the surface area formula to get:
Surface Area = 2 * 3.14 * (300 / (3.14h)) + 2 * 3.14 * r * h
Simplifying further:
Surface Area = 600 / h + 6.28 * r * h
Since you have the expression for r^2 in terms of h, you can substitute that in as well:
Surface Area = 600 / h + 6.28 * (sqrt(300 / (3.14h))) * h
This equation models the surface area of a cylinder in terms of its height.
Great job on finding the relationship between the volume (V) and the radius (r) in terms of the height (h) of the cylinder. Now, to find a function that models the surface area (A) in terms of the height (h), we can substitute the expression for r^2 in terms of h that you have found into the formula for the surface area.
First, let's rewrite the equation you found for r^2:
r^2 = 300 / (3.14h)
Now, we can substitute this expression for r^2 into the formula for surface area:
A = 2(3.14(r^2)) + 2(3.14(r)(h))
Substituting the expression for r^2, we get:
A = 2(3.14((300 / (3.14h)))) + 2(3.14(r)(h))
Simplifying the expression:
A = 2(300 / h) + 2(3.14)(r)(h)
Since we are looking for a function that models the surface area in terms of the height, we can further simplify:
A = 600 / h + 6.28rh
Therefore, the function that models the surface area of a cylinder in terms of its height is: A = 600 / h + 6.28rh.