Answer:
First, we need to convert all the measurements to the same unit. Let's convert everything to inches, since the formula for the volume of a cylinder uses inches:
12 in = 12 in
14 in = 14 in
12 in = 12 in
4 in = 4 in
The object consists of a cylinder with a radius of 4 inches and a height of 12 inches, and a hemisphere with a radius of 4 inches. To find the volume of the object, we need to find the volume of the cylinder and the hemisphere, and then add them together.
Volume of the cylinder:
V_cyl = πr^2h
V_cyl = π(4 in)^2(12 in)
V_cyl = 192π in^3
Volume of the hemisphere:
The volume of a hemisphere is given by:
V_hemi = (2/3)πr^3
Since the radius is 4 inches, we have:
V_hemi = (2/3)π(4 in)^3
V_hemi = (2/3)π(64 in^3)
V_hemi = 128π/3 in^3
Total volume:
V_total = V_cyl + V_hemi
V_total = 192π in^3 + 128π/3 in^3
V_total = (576π + 128π)/3 in^3
V_total = 704π/3 in^3
Now we can substitute the value of π (3) to get the final answer:
V_total = 704π/3 in^3
V_total = 704(3)/3 in^3
V_total = 704 in^3
Therefore, the volume of the object is 704 cubic inches.