Kaci bought a birthday cake, like the one shown below, for her mother.
Note: Figure is not drawn to scale.
If a = 5 inches, b = 5 inches, c = 9 inches, and d = 3 inches, what is the volume of the cake?
To find the volume of the cake, we need to find the volume of the rectangular prism and the volume of the cylinder separately, and then add them together.
Volume of the rectangular prism:
V_rectangular prism = length x width x height
V_rectangular prism = a x b x c
V_rectangular prism = 5 x 5 x 9
V_rectangular prism = 225 cubic inches
Volume of the cylinder:
V_cylinder = πr^2h
First, we need to find the radius of the cylinder, which is half of d.
r = d/2
r = 3/2
r = 1.5 inches
V_cylinder = π(1.5)^2(9)
V_cylinder = π(2.25)(9)
V_cylinder = π(20.25)
V_cylinder ≈ 63.28 cubic inches
Total volume of the cake:
V_total = V_rectangular prism + V_cylinder
V_total = 225 + 63.28
V_total ≈ 288.28 cubic inches
Therefore, the volume of the cake is approximately 288.28 cubic inches.