If a cone has the same radius and height as a cylinder, the volume of the cone is one-fourth one-third half two-thirds 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 one-fourth one-third half two-thirds the volume of the cylinder.

The volume of the cone is one-third the volume of the cylinder, if both shapes have the same radius and height

The volume of a cone is represented as:

v = 1/3r^2h

The volume of a cylinder is represented as:

V = r^2h

Substitute r^2h for V in the volume of the cone

v = 1/3V

The above means that:

The volume of the cone is one-third the volume of the cylinder

Read more about volumes at:

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∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.