Question

Is my data correct?

For package design I will use a cylinder. The Equation for the surface area of a cylinder is A = 2 π r h + 2 π r² . The equation for the volume of a cylinder is V = π r² h. I have chosen a cylinder for my cereal box because I believe a cylinder can hold the most cereal in the most efficient way.



Dimentions of a regular cereal box
length 19cm
width 6cm
height 27cm


Volume of a rectangular prism equation V = l · w · h.
V = 19 · 6 · 27 = 1539.

The Volume of a regular cereal box is 3078 cubic inches

Surface area of a rectangular prism formula A = 2(w · l + h · l + h · w)


A = 2( 6 · 19 + 27 · 19 + 27 · 6)
A = 1578.

The Surface area is 1578cm²

Conversion factor 1inch = 2.5 cm

I will divide the surface area by 2.5 to get how many inches.
1578 / 2.5 = 631.2

I will then multiply 631.2 by .5 to see how much it would cost to make a regular cereal box.

631.2 · .5 = 315.6

To Manufacture a regular sized cereal box it would take $31.56.



My Cereal box is a cylinder

Length 4cm
Width 20cm
Height 11cm

V=π r² h
V= π ·102 · 11 ≈3455.75192

The volume of my cylinder cereal box is 3455.75 cubic inches

Surface area of a cylinder A = 2 · π · r · h + 2 · π · r²

A = 2 · π · 10 · 11 + 2 · π · 10² ≈ 1319.46891

The Surface area of my cylinder is 1319.47 cm²

I will follow the same steps I did before

Convert from cm to inches
1319.47 / 2.5 = 527.788

Then 527.788 · .5 = 263.894

It would take approximately $26.39 to manufacture my cylinder cereal box.

Answer 1

you are correct that a cylinder has less surface area than a rectangular prism.