Question

1. which factor directly explains why the volume of a cone is smaller than that of a cylinder with the same base and height?

a. a cone has a smaller base.
b. a cone has a smaller height.
c. all cones are smaller than all cylinders.
d. a cone tapers to a point, taking up less space.

Explanation:

The volume formula for a cylinder is \(V_{cylinder}=\pi r^{2}h\) (where \(r\) is the radius of the base and \(h\) is the height). The volume formula for a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). When they have the same base (\(r\) is the same) and height (\(h\) is the same), the difference in volume is due to the geometric shape. A cone tapers to a point, which means it takes up less space compared to a cylinder with the same base and height. Option a is incorrect because the problem states "with the same base". Option b is incorrect because the problem states "with the same height". Option c is incorrect as it is a general and untrue statement (e.g., a very large - radius, short - height cone could have a larger volume than a very small - radius, tall cylinder in some non - same base and height cases).

Answer:

d. A cone tapers to a point, taking up less space.