Final answer:
To compute the surface area of the cone generated by revolving the function c(t) = t², use the formula A = πr(r + √(r² + h²)), where r is the radius of the base and h is the height of the cone.
Step-by-step explanation:
To compute the surface area of the cone generated by revolving the function c(t) = t², we can use the formula for the surface area of a cone. The formula is given by A = πr(r + √(r² + h²)), where r is the radius of the base and h is the height of the cone.
In this case, the function c(t) = t² represents the radius of the base of the cone as a function of the height. So, we need to find the derivative of c(t), which is 2t. This gives us the radius as a function of height, r = 2t.
Substituting this into the formula, we get A = π(2t)(2t + √((2t)² + h²)).