Answer:
413.9 cm²
Step-by-step explanation:
The total surface area of the solid is the sum of the curved area, semicircular end area, and rectangular base area.
Half a cylinder
The area of the curved surface is the lateral area of half a cylinder. The area of the semicircular ends is half the end area of a cylinder. The area of these surfaces together is half the area of a cylinder:
A = 1/2(2πr)(r +h) = πr(r +h)
The radius is half the given diameter, so the area of the half-cylinder we can see is ...
A = π(3 cm)(3 cm +25 cm) = 84π cm²
Rectangular base
The rectangular bottom of the figure is hidden from view. Its dimensions are given as 6 cm wide by 25 cm long. Its area is given by the formula for the area of a rectangle:
A = LW
A = (25 cm)(6 cm) = 150 cm²
Total area
The total surface area of the figure is the sum of the half-cylinder area and the area of the base:
total area = (84π +150) cm² ≈ 413.9 cm²
The surface area of the figure is about 413.9 square centimeters.
