A bottle of perfume is made up of a triangular prism exterior with a cylindrical interior that holds the perfume. What is the volume of the cylinder? The dimensions are length=4 in.; width=3 in.; height=5 in.; and diameter=2.6 in
First, let's calculate the volume of the triangular prism exterior. The formula for the volume of a triangular prism is V = 0.5 * length * width * height.
Given: length = 4 in, width = 3 in, height = 5 in
V = 0.5 * 4 * 3 * 5
V = 0.5 * 60
V = 30 cubic inches
Now, let's calculate the volume of the cylinder interior. The formula for the volume of a cylinder is V = π * radius^2 * height.
Given: diameter = 2.6 in, so radius = 2.6 / 2 = 1.3 in, height = 5 in
V = π * (1.3)^2 * 5
V = π * 1.69 * 5
V = 8.45π cubic inches
Therefore, the volume of the cylinder interior is approximately 8.45π cubic inches.