A canning company has hired you to design labels for their food cans. You need to know how big the labels are. You know the formula for determining the lateral surface area of a cylinder is S = 2 pie rh. The cans ( h ) height measures 4 " and its ( d ) diameter is 3 " . You also know that the ( r ) radius is half of the diameter. How big will your label be?
2006-08-05 03:25:16 · 7 answers · asked by Anonymous in Education & Reference ➔ Homework Help
this is relatively simple isnt it since the formula and all necessary information is all there in the question. all you have to do is plug in the values.
2 pi r h = 2 x pi x 1.5 x 4 = 12pi sqinches.
2006-08-05 06:48:14 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The formula is correct, surface area of a cylinder is the circumference times height. (C=d pi or C = 2pi r) Multiplying the inches in the circumference times the inches in the height will give you your inches squared. =)
If I understood you correctly, the label will cover the entire can.
since you know s = 2pi r h
and h = 4
d= 3 but d = 2r
we can rewrite the original formula
s = pi dh
so s = pi *3*4 or 12 pie. You can get an approximate answer by using a calculator: 37.79 sq inches
However as a designer this information would not help you. You are better off just knowing the dimensions and envisioning the label flat.
You need to know the height of the can and the circumference of it. Circumference is just dpi (or 2r pi) and height you were given.
So for practical design purposes the label is 9.42 inches by 4 inches.
2006-08-05 10:36:21 · answer #2 · answered by goodlittlegirl11 4 · 0⤊ 0⤋
Ok, now put it all together. Since the radius is half the diameter and 2 half equal a whole, that is 2r = the diameter or 3". Put the rest into the formula. Pi times the Height times Diameter =.
Now just do the math. Pi = 3.14
2006-08-05 10:37:32 · answer #3 · answered by Dennis Fargo 5 · 0⤊ 0⤋
2*pi*(.5*3)*4 = 12 pi = 37.7 Sq inches = 4 inches * 9.42...inches
That is the surface area of the can on the side. But if you are designing a can to be glued to the can, there MUST be overlap (for the glue). Unless this is a simple math problem, there must be consideration for overlap.
If overlap is needed, add to the 9.42 inches to compensate.
10 inches would be sufficient.
Therefore the labels would be 4 inches by 10 inches.
2006-08-05 11:36:38 · answer #4 · answered by vector4tfc 4 · 0⤊ 0⤋
2 * pi * (3 * .5) * 4
12pi inches
according to what you've given for the surface area formula. But area is square inches, I think the r should be squared. Therefore:
2 * pi * ((3 * .5)^2) * 4
18pi sqin
2006-08-05 10:35:54 · answer #5 · answered by Anonymous · 0⤊ 0⤋
123
2006-08-05 10:36:49 · answer #6 · answered by Anonymous · 0⤊ 0⤋
S=2pi rh
h- 4
d- 3
r- 1.5
2(pi)(1.5)(4)
= 12pi
2006-08-05 10:47:17 · answer #7 · answered by crestfallen 5 · 0⤊ 0⤋