Answer :
Questions relating Word Problems can sometimes be resolved by taking note of the definition of given clues
The amount of soda lost is approximately 28.27 in.³
The reason the above value is correct is as follows:
The known parameters about the the soda pop served by the restaurant are;
Diameter of the cylindrical pitcher in which the soda pop is sold, D = 6 inches
The height of the cylindrical pitchers, h = 8 inches
Thickness of the head of foam in the pitchers, t = 1 inches
Required:
The amount of soda lost as a result of the head of foam
Method:
Define a pitcher
Calculate the volume occupied by the head of foam
Solution:
A pitcher holds drink and usually has a lip and handle, therefore, the drink is filled level with the pitcher
The volume occupied by the head of foam = The amount of soda lost
The volume occupied by the head of foam, [tex]\mathbf{V_{(head \ of \ foam)}}[/tex] = The volume of 1 inch height of the foam in the cylindrical pitcher
Volume in a cylinder = Base area × Height
[tex]\mathbf{Base \ area\ in \ a \ cylinder} =\dfrac{\pi \cdot D^2}{4}[/tex]
The height of the foam = The thickness of the foam = t
∴ [tex]V_{(head \ of \ foam)} =\mathbf{\dfrac{\pi \cdot D^2}{4} \times t}[/tex] =
Plugging in the values of D, and t, gives;
[tex]\mathbf{V_{(head \ of \ foam)}} =\dfrac{\pi \times (6 \ in.)^2}{4} \times 1 \ in. = \pi \mathbf{\times 9 \, in.^3}[/tex]
The volume of the head of foam, given to two decimal places is presented as follows;
[tex]V_{(head \ of \ foam)}[/tex] = π × 9 in.³ ≈ 28.27 in.³
The volume of the head of foam = The amount of soda lost ≈ 28.27 in.³
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