A baker drew a design for a 2-tier wedding cake with a prism-shaped cake as the first tier and a cylinder-shaped cake as the second tier, as shown above. Based on the design, what is the total volume of the wedding cake? Use 3.14 for pi and round your answer to the nearest tenth.
To find the volume of each tier, we need to use the formulas for the volume of a prism and a cylinder.
Prism-shaped tier:
Height = 8 inches
Base area = (6 inches) * (6 inches) = 36 square inches
Volume = Base area * Height = 36 sq in * 8 in = 288 cubic inches
Cylinder-shaped tier:
Height = 6 inches
Base area = pi * (3 inches)^2 = 28.26 square inches
Volume = Base area * Height = 28.26 sq in * 6 in = 169.6 cubic inches
Total volume = 288 cubic inches + 169.6 cubic inches = 457.6 cubic inches
Rounded to the nearest tenth, the total volume of the wedding cake is approximately 457.6 cubic inches.