Answer:
1.243 cm
Step-by-step explanation:
The surface area of a cylinder is the sum of the area of the two congruent circular bases and the rectangular lateral area.
[tex] SA = 2\pi r^2 + 2 \pi rh [/tex]
[tex] SA = 2\pi r(r + h) [/tex]
We are given the surface area and the diameter.
r = d/2 = 7 cm / 2 = 3.5 cm
We can solve for h, the height.
[tex] SA = 2\pi r(r + h) [/tex]
[tex] 2\pi r(r + h) = SA [/tex]
[tex] r + h = \dfrac{SA}{2\pi r} [/tex]
[tex] h = \dfrac{SA}{2\pi r} - r [/tex]
[tex] h = \dfrac{104.3~cm^2}{2(3.14159)(3.5~cm)} - 3.5~cm [/tex]
[tex] h = 1.243~cm [/tex]
