The surface area S of a cylinder is given by the formula S = 2 π rh + 2 πr^2
Write the formula for S in terms of the radius if the height of the cylinder is 5 more than 3 times its radius. keep the answer as S=....
Use the symbol for pi (distribute out and write answer as an expanded polynomial)
S = 2 π r(3r+5) + 2 πr^2
so, expanded, that is
S = 8πr^2 + 10πr
4
To write the formula for S in terms of the radius, we need to express the height in terms of "r" first. We are given that the height of the cylinder is 5 more than 3 times its radius. Let's represent the height as "h" and the radius as "r". According to the given information, we have:
h = 3r + 5
Now, substituting this height value into the surface area formula S = 2πrh + 2πr^2, we get:
S = 2πr(3r + 5) + 2πr^2
To simplify further, we can distribute the 2πr to both terms inside the parentheses:
S = 2πr * 3r + 2πr * 5 + 2πr^2
This gives:
S = 6πr^2 + 10πr + 2πr^2
Finally, combining like terms, we can simplify the expression:
S = (6π + 2π)r^2 + 10πr
Therefore, the formula for the surface area S, in terms of the radius "r," is:
S = (8π)r^2 + 10πr