A package of aluminum foil contains 50. ft2 of foil, which weighs approximately 8.5 oz . aluminum has a density of 2.70 g/cm3. what is the approximate thickness of the foil in millimeters?

Respuesta :

Hello!

We have the following data:

Area (A) = 50 square feet
Mass (m) = 8.5 ounces
Density (d) = 2.70 g/cm³
Volume (V) = ?
Thickness (T) =? (in mm)

To move on, we must transform the area of 50 ft² in cm², let's see:

1 ft² ------- 929,0304 cm²
50 ft² ----- A

[tex]A = 50*929,0304[/tex]

[tex]\boxed{A = 46451,52\:cm^2}\Longleftarrow(Area)[/tex]

In the same way, we will convert the mass of 8.5 oz in grams, see:

1 oz -------- 28,3495 g
8,5 oz ------- m

[tex]m = 8,5*28,3495 [/tex]

[tex]\boxed{m = 240,97075\:g}\Longleftarrow(mass)[/tex]

Knowing that the density is 2.70 g/cm³ and the mass is 240.97075 g, we will find the volume, applying the data in the density formula we have:

[tex]d = \dfrac{m}{V} \to V = \dfrac{m}{d} [/tex]

[tex]V = \dfrac{240,97075\:\diagup\!\!\!\!\!g}{2,70\:\diagup\!\!\!\!\!g/cm^3} [/tex]

[tex]V = 89,24842593... \to \boxed{V \approx 89,25\:cm^3}[/tex]

The statement wants to find the thickness of the packaging, for this we have some important data, such as: V (volume) = 89,25 cm³ and Area (A) = 46451,52 cm² and T (thickness) =? (in mm)

In the calculations of Costs in Surface Treatment of a part within the flat geometry, we will use the following formula:

[tex]V (volume) = A (Area) * T (Thickness)[/tex]

[tex]89,25\:cm^3 = 46451,52\:cm^2\:*\:T[/tex]

[tex]46451,52\:cm^2*T = 89,25\:cm^3[/tex]

[tex]T = \dfrac{89,25\:cm^3}{46451,52\:cm^2} [/tex]

[tex]T = 0,001921358009...\:cm[/tex]

We will convert to millimeters, going through a decimal place on the right

[tex]T = 0,01921358009..\:mm [/tex]

[tex]\boxed{\boxed{T \approx 0,0192\:mm\:or\:T\approx \:1,92*10^{-2}\:mm}}\end{array}}\Longleftarrow(thickness)\qquad\checkmark[/tex]

Hope this helps! :))





Answer: 1.5 • 10^ -2

Explanation:

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