Asandwich shop uses the box size shown to pack boxed lunches. they have determined that they need to use bigger boxes. if the side lengths of the square faces are changed to 7 inches, by how much will this increase the volume of the box?

240 cubic cm

Step-by-step explanation:

Volume of the box before increament in sides = length*width*height

Length= 5 in.

Width=5 in.

Height = 10 in.

Putting these vales in formula

Volume of box = 5*5*10

                        =

Now  If the side lengths of the square faces are changed to 7 inches,

So, Length will be 7 in.

Width will be 7 in.

So, new volume = 7*7*10

                          =

Thus increase in volume = 490-250 =240

Hence by 240 cubic cm  will this increase the volume of the box

∠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.