Final answer:
The volume of a cone with a diameter of 5 inches and a height of 18 inches is calculated by converting dimensions to millimeters, applying the volume formula, and obtaining a result of approximately 1,929,571.86 mm^3, which corresponds to the answer 'None of these'.
Step-by-step explanation:
The question seeks to calculate the volume of a cone in cubic millimeters, given its dimensions in inches, using the formula V=pi*r^2*(H/3) and the conversion factor 1 inch = 25.4 mm. To solve for volume, we make use of dimensional analysis and convert the measurements of the cone from inches to millimeters before applying the formula.
First, we find the radius of the cone by dividing the diameter by 2, which gives us a radius of 2.5 inches. We then convert this radius into millimeters: 2.5 inches * 25.4 mm/inch = 63.5 mm. After that, we convert the height into millimeters: 18 inches * 25.4 mm/inch = 457.2 mm.
Finally, we apply the volume formula as follows:
V = pi * (63.5 mm)^2 * (457.2 mm / 3)
Calculating this gives us:
V = 3.14159 * (63.5 mm)^2 * (457.2 mm / 3)
V = 3.14159 * 4032.25 mm^2 * 152.4 mm
V = 3.14159 * 614,184.81 mm^3
V = 1,929,571.86 mm^3
Thus, the correct answer is None of these, as none of the options provided match the calculated volume of the cone.