A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:
A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]
where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:
l = w = 16 in
h = 15 in
Substituting:
A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]
A = 256 + 272 + 272
A = 800 in^2
B. We are given a cone, the formula for surface area is:
A = πr (r + h^2 + r^2)
where h is the height = 8 in and r is the radius = 3 in
Substituting:
A = π * 3 (3 + sqrt (8^2 + 3^2))
A = 34.63π in^2 = 108.80 in^2