Final answer:
The height of the cylinder with a radius of 15 cm and a surface area of 2040π cm² is found to be 53 cm by rearranging and solving the surface area formula for the height.
Step-by-step explanation:
To find the height of the cylinder, we can rearrange the surface area formula SA = 2πr^2 + 2πrh, where SA is the surface area, r is the radius, and h is the height. Given that SA = 2040π cm² and r = 15 cm, we can plug these values into the formula to get 2040π cm² = 2π(15 cm)^2 + 2π(15 cm)h. Simplifying the equation yields 2040π cm² = 450π cm² + 30πh cm². Subtracting 450π cm² from both sides gives us 1590π cm² = 30πh cm², and dividing both sides by 30π cm² results in h = 53 cm, which is the height of the cylinder.
To find the height of the cylinder, we can use the formula for the surface area of a cylinder and the given information. The formula for the surface area is SA = 2πr^2 + 2πrh, where r is the radius and h is the height. We are given that the radius is 15 cm and the surface area is 2,040π cm². Plugging in these values, we get:
2040π = 2π(15^2) + 2π(15h)
1020 = 225 + 30h
30h = 795
h = 795/30
h ≈ 26.5 cm