Gold in the form of solid cylinders will be molded into solid blocks. each cylinder has a diameter of 6.18 cm and a height of 6 cm. each solid block will have a volume of 360 cm3. how many cylinders of gold will it take to mold one block of gold?

First we need to find out the volume of one cylinder. We already know the volume of the block of gold is 360cm3

V = Pie * radius squared* height.

Pie is 3.142

radius is 6.18/2 = 3.09 cm

height is 6cm

V = 3.142 * 3.09 * 3.09 * 6

V = 180cm3

Now we divide the volume of this cylinder with the volume of block of gold.

360/180 = 2

So it will take 2 cylinders to mold one block of gold.

∠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.