Question

the volumeof a cylinder is 216 inches cubic what is the volume of a cone with the same radius and height as the cylinder?

Answer 1

The volume of the cone with the same radius and height as the given cylinder is 54.99 cubic inches.

Step-by-step explanation:

To find the volume of a cone with the same radius and height as the given cylinder, we need to use the formulas for the volumes of cylinders and cones. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Given that the volume of the cylinder is 216 cubic inches, we can solve for the radius by rearranging the formula: r = sqrt(V/(πh)). Plugging in the values, we find r = sqrt(216/(3.142*5.25)) = 3 inches. Now that we have the radius, we can find the volume of the cone using the formula V = (1/3)πr²h. Substituting the values, we get V = (1/3)*3.142*(3²)*5.25 = 54.99 cubic inches.

Answer 2

The answer is 72 cubic inches. This is because the formula for the volume of a cylinder is πr² × h, and the formula for the volume of a cone is (πr² × h)/3. This means that the volume of a cone with the same height and radius as the cylinder will just be a third of the volume of the cylinder, so we need to divide 216 by 3 which equals 72.
I hope this helps!