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 = (1/2) * base * height * length.
Given that the base is a triangle with a width of 3 in. and a height of 5 in., we can calculate the area of the base:
Area = (1/2) * base * height = (1/2) * 3 * 5 = 7.5 sq. in.
Now, multiplying the area of the base by the length of the prism (4 in.), we can find the volume of the triangular prism exterior:
V = 7.5 sq. in. * 4 in. = 30 cubic inches.
Next, we calculate the volume of the cylinder interior using the formula for the volume of a cylinder: V = π * r^2 * h, where r is the radius and h is the height.
Given that the diameter of the cylinder is 2.6 in., the radius is half of the diameter, so r = 2.6 in. / 2 = 1.3 in.
Now, substitute the values into the formula:
V = π * (1.3 in.)^2 * 5 in.
V = π * 1.69 sq. in. * 5 in.
V ≈ 8.45 cubic inches
Therefore, the volume of the cylinder interior that holds the perfume is approximately 8.45 cubic inches.