Your goal is to design a new shape for a cereal container that will hold the same volume of cereal as a standard ceareal box and costs as little as possible to make. Assume that cardboard costs $0.05 per square inch. How cheaply can you package cereal? These figures are available.
* triangular prism
* rectangular prism
* cube
* pyramid
* cone
* cylinder
* sphere

You need to keep the volume the same as the original, the surface area has to be less, and the price has to be the cheapest. The original volume was 192in^3. The surface area was 272in^2.

$14.50

Step-by-step explanation:

To calculate the cost for manufacturing a standard cereal box, we must take in account its surface area. The volume will be used to estimate the amount of cereal, the box can contain. The box is a cuboid as standard cereal boxes are cuboid.

So, we will consider the surface area. Given are:

Length- 8 inches

Width- 3 inches

Height- 11 inches

We will find the surface area as : 2lw + 2wh +2lh

= (2x8x3) + (2x3x11) + (2x8x11)

= 48 + 66 + 176 = 290 square inches

Given is - the cost of manufacturing the box is $0.05 per square inch.

So, cost of manufacturing the box with 290 square inches area =

0.05 x 290 = $14.50

The answer is $14.50

x/7.50 = 15

x= 7.50 / 15 divide

step-by-step explanation:

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.