Question

Select the correct answer from each drop-down menu:If a cone has the same radius and height as a cylinder, the volume of the cone is ______ the volume of the cylinder. If a cylinder and a sphere have the same radius and the cylinder's height is twice its radius, then the volume of the sphere is ____ the volume of the cylinder.

Answer 1

A) one-third

B) two-thirds

Step-by-step explanation

FIRST QUESTION

The volume of a cone is given as:

`V\text{ = }(1)/(3)\pi r^2h`

and the volume of a cylinder is given as:

`V\text{ = }\pi r^2h`

where r = radius

h = height

If a cone has the same radius and height as a cylinder, it means that r = r and h = h.

Therefore, comparing the volumes, we have that the volume of the cone will be 1/3 of the volume of the cylinder.

The correct option is one-third.

SECOND QUESTION

The volume of a sphere is given as:

`V\text{= }(4)/(3)\pi r^3`

We have already stated the volume of a cylinder above.

If the height of a cylinder is twice its radius, it means:

h = 2r

Therefore:

`\begin{gathered} V\text{ = }\pi\cdot r^2\cdot\text{ 2r} \\ \text{V = 2}\pi r^3\text{ }^{}^{} \end{gathered}`

If the radius of a cylinder and sphere are the same, it means r = r.

Therefore, comparing the volumes, we see that the volume of the sphere is 2/3 times that of a cylinder.

The correct option is two-thirds.