Explanation:
a) The total surface area is the sum of the 3 lateral rectangular sides, 2 triangular bases minus the circle, and lateral surface of the hole.
Area of each rectangular side is cL = (6)(8) = 48 square units.
Area of the each triangular base is ¼√3 c² = ¼√3 (6)² = 9√3 square units.
Area of the circle is A = c² = π (2)² = 4π square units.
Area of the hole is 2πrL = 2π (2)(8) = 32π square units.
Therefore the total area is:
SA = 3(48) + 2(9√3 − 4π) + 32π
SA = 144 + 18√3 + 24π
SA ≈ 250.58 square units
b) The volume is the area of the base times the length of the prism.
The area of the base is the area of the triangle minus the area of the circle.
V = (9√3 − 4π) (8)
V = 72√3 − 32π
V ≈ 24.18 cubic units