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A Styrofoam cooler has outside dimensions of B = 84.0 cm, W = 47.0 cm, and H = 59.0 cm. The thickness of each wall of the cooler, t, is 8.0 cm. Styrofoam has a density, rho, of 1.0 kg/m3. (a) What is the volume of the Styrofoam used in cubic inches? (b) What is the mass in lbm? (c) How many gallons of liquid could be stored in the cooler?

(a) The volume of the Styrofoam used is 14214.37 in3.
(b) The mass is 9.6 lbm.
(c) The number of gallons of liquid that could be stored in the cooler is 1058.54 gal.

Respuesta :

Answer:

a) [tex]V_s=4989.7895\ in^3[/tex]

b) [tex]mass=0.1803\ lb[/tex]

c) [tex]V_i=39.93\ gallons[/tex]

Explanation:

  • external breadth of cooler, [tex]B=84\ cm[/tex]
  • external width of cooler, [tex]W=47\ cm[/tex]
  • external height of cooler, [tex]H=59\ cm[/tex]
  • ∵ thickness of each wall is, [tex]t=8\ cm[/tex]

Therefore,

  • internal breadth of cooler, [tex]B_i=76\ cm[/tex]
  • internal width of cooler, [tex]W_i=39\ cm[/tex]
  • internal height of cooler,  [tex]H_i=51\ cm[/tex]

a)

External volume of the structure:

[tex]V=B.H.W[/tex]

[tex]V=84\times47\times59\div 2.54^3[/tex]

[tex]V=14214.3828\ in^3[/tex]

Internal volume of the structure:

[tex]V_i=B_i.H_i.W_i[/tex]

[tex]V_i=76\times 39\times 51\div 2.54^3[/tex]

[tex]V_i=9224.5932\ in^3[/tex]

∴Volume of Styrofoam used:

[tex]V_s=V-V_i[/tex]

[tex]V_s=14214.3828-9224.5932[/tex]

[tex]V_s=4989.7895\ in^3[/tex]

b)

given that density of Styrofoam, [tex]\rho=1\ kg.m^{-3}=3.613\times 10^{-5}\ lb.in^{-3}[/tex]

we know,

[tex]\rm mass= density \times volume[/tex]

[tex]mass=4989.7895\times 3.613\times 10^{-5}[/tex]

[tex]mass=0.1803\ lb[/tex]

c)

Volume of liquid it can hold [tex]=V_i[/tex]

[tex]V_i=39.93\ gallons[/tex]

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