Final answer:
The volume ratio of a cone to a cylinder with the same radius and height is 1:3, since the cone's volume is one-third that of the cylinder.
Step-by-step explanation:
To find the volume ratio of a cone to a cylinder with the same radius, we must understand their volume formulas. The volume of a cylinder (Vcylinder) is given by the formula V = πr²h, and the volume of a cone (Vcone) is given by V = (1/3)πr²h, where π is approximately 3.14, r is the radius, and h is the height. Since both the cone and the cylinder have the same radius and height, we can compare their formulas directly.
The cylinder's volume is simply πr²h, and the cone's volume is (1/3) of the cylinder's volume because of the (1/3) factor in its formula. Therefore, the volume ratio of the cone to the cylinder is 1:3, which means for any given height, the cone will have one-third the volume of the cylinder with the same radius. The correct answer to the question is (a) 1:3.