We can separate this solid into two pieces: a cylinder and a cone. I will be finding the surface area's separately, then adding them together in the end.
<u>Cylinder:</u> The formula for the surface area of a cylinder is 2πrh+2πr². HOWEVER, since the cone and cylinder are connected, they don't count as part of the surface area, we don't need the 2 in 2πr². Therefore, the formula is 2πrh+πr². The radius, or r, is 10 cm. The height, or h, is 16 cm. We use those numbers and plug it in the formula:
2πrh+πr²
2π(10)(16)+π(10)²
320π+100π
420π cm²
<u>Cone:</u> The surface area of the cone without its base is πrL where r is the radius (10) and L is the slant length (13)
π·10·13 = 130π cm²
Total: We add the total SA of the cylinder and the cone together to find the total: 420π+130π=550π=550·3.14 ≈ 1727 cm²
