Calista selects a box with a volume of Sin.3 to package her first order. • What is the length of each side of the box Calista selected?

• The items for Calista's order do not fit in her box. She needs a box that will hold

another 56in.3 of space. What would the length of each side of this box need to be?

Show the work to explain your answer.

• For her next order, Calista has three cube-shaped objects that need to be packed

into the same box. of the objects have a volume of 8in.3 The third object has a

volume of 27 in 3 What can be the minimum length of each side of the box? Show the

work to explain your answer.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction