The surface area S of a cylinder is given by the formula S = 2 π rh + 2 πr Write the fomula for S in terms of the radius if the height of the cylinder is S more than 3 times its radius. Use the symbol for pi (distribute out and write answer as an expanded polynomial)
Actually, S = 2πrh + 2πr^2
How can the height be more than the surface area? You clearly have a typo. I'll say that h = 3r+x, and you can fill in what you meant to say.
Thus we have
S = 2πr(3r+x) + 2πr^2
S = 8πr^2 + 2πxr
Let's break down the information given:
The height of the cylinder is S more than 3 times its radius, which can be represented as:
h = 3r + S
Now, substituting this value of h into the surface area formula:
S = 2πrh + 2πr
Substituting (3r + S) for h:
S = 2πr(3r + S) + 2πr
Expanding the expression:
S = 6πr^2 + 2πrS + 2πr
Therefore, the formula for the surface area S in terms of the radius when the height of the cylinder is S more than 3 times its radius is:
S = 6πr^2 + 2πrS + 2πr
To find the surface area of a cylinder, we can use the formula S = 2πrh + 2πr, where S represents the surface area, r represents the radius, and h represents the height of the cylinder.
In this case, we are given that the height of the cylinder is S more than 3 times its radius, so we can express the height as h = 3r + S.
Now, we can substitute the value of h in the surface area formula:
S = 2πr(3r + S) + 2πr
To simplify, let's distribute the 2πr to each term inside the parentheses:
S = 6πr^2 + 2πrS + 2πr
Finally, we can rearrange the terms and write the answer as an expanded polynomial:
S = 6πr^2 + 2πrS + 2πr
Therefore, the formula for the surface area S in terms of the radius when the height is S more than 3 times the radius is:
S = 6πr^2 + 2πrS + 2πr