Question

What is the surface area of the cylinder? Please show work.

Answer 1

Surface area is 288π cm² (exact solution), which is approximately 904.78 cm² (if you use pi on calculator) or 904.32 cm² (if you use 3.14 for pi).

Explanation:

Surface area of cylinder

`SA = 2 * \text{area of base} + \text{lateral area}\\SA = 2 \pi r^2 + 2 \pi r h`

SA ... surface area

r ... radius

h ... height of cylinder

Given:

d = 12 cm

h = 18 cm

Since diameter d is 12 cm, that means that radius is half of that, so 6 cm.

r = 6 cm

Insert in formula:

`SA = 2 \pi r^2 + 2 \pi r h\\SA = 2 \pi (6)^2 + 2 \pi (6)(18)\\SA = 72 \pi + 216 \pi\\SA = 288 \pi \text{ cm}^2 \approx 904.78 \text{ cm}^2`