Omg please please please help me I really really really need help on this. Please can you guys help me solve this problem?

The volume of the figure is: 60840, or approximately about 191037.6 ft^3.

Step-by-step explanation:

This 3D figure can be split into two separate figures, a half-sphere, and a cone.

Let's first try to find the volume of the half-sphere.

The formula for the volume of the half-sphere is , so substituting 39 for r gives us a volume of 39546ft^3, or about 124174.44 ft^3.

Next, let's find the volume of the cone. We see that the radius of the cone is once again 39 ft, and the height of the cone i s just 81-39, or 42 ft.

The volume of a cone is , and substituting 39 for r and 42 for h, we obtain a result of 21294, or about 66863.16

Thus, the final volume of the figure is: 60840, or approximately about 191037.6 ft^3

∠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.