The height of the cone is 6 m, the diameter of the base is 16 m. Find the areas of the lateral and total surfaces of the cone.

The total surface area of the cone is calculated by the formula:

S full = S side + S main.

Side surface area S side = pi * r * l.

The area of the base of the cone Sbn = pi * r ^ 2.

The radius r of the base of the cone is r = 16/2 = 8 m.

Let S be the apex of the cone, O the center of the base, SO the height of the cone h, OA the radius of the circle r, AS the generatrix of the cone l.

Then, from a right-angled triangle OSA, the generator is equal to

l = ((h) ^ 2 + (r) ^ 2) ^ (1/2) = (6 ^ 2 + 8 ^ 2) ^ (1/2) = 10 m.

Hence,

S main = pi * 8 ^ 2 = 64 * pi.

Side = pi * 8 * 10 = 80 * pi.

S total = 80 * pi + 64 * pi = 144 * pi.