ANSWER
A) one-third
B) two-thirds
EXPLANATION
FIRST QUESTION
The volume of a cone is given as:
[tex]V\text{ = }\frac{1}{3}\pi r^2h[/tex]
and the volume of a cylinder is given as:
[tex]V\text{ = }\pi r^2h[/tex]
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:
[tex]V\text{= }\frac{4}{3}\pi r^3[/tex]
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:
[tex]\begin{gathered} V\text{ = }\pi\cdot r^2\cdot\text{ 2r} \\ \text{V = 2}\pi r^3\text{ }^{}^{} \end{gathered}[/tex]
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.
