Question

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Determine if each statement is always, sometimes, or never true​

Answer 1

1. Sometimes
2. Sometimes
3. Always

Lets note the formulas first to make clear.

For cone

• V=1/3πr²h

For cylinder

• V=πr²h

For sphere

• V=4/3πr³

We can see

for first two

• the volume depends upon the height hence if they have same radius then their volume may or may not be same

For sphere

• volume depends upon radius so if radius is same the volume is same

Answer 2

1. sometimes
2. sometimes
3. always

Explanation:

These questions can be answered by reference to the formulas for the volume of a cone, cylinder, and sphere.

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Cone

V = 1/3πr²h . . . volume depends on height as well as radius

Cones with the same radius will sometimes have the same volume. (When they have the same height.)

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Cylinder

V = πr²h . . . volume depends on height as well as radius

Cylinders with the same radius will sometimes have the same volume. (When they have the same height.)

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Sphere

V = 4/3πr³ . . . volume depends only on radius

Spheres with the same radius will always have the same volume.