Jack J.

asked • 03/21/16

food box is a similar shape to a water box.volume of the water box is 3/4 of the volume of the food box.SA of the water box is 628cm2.SA of food box?

The eating space of the chicken coop also has a feed container. The feed container is similar in shape to the water container. The volume of the water container is three-quarters of the volume of the feed container. The surface area of the water container is 628 cm2. What is the surface area of the feed container?

1 Expert Answer

By:

Elwyn D. answered • 03/21/16

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AntoriaGirl B.

how? 
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03/21/16

Elwyn D.

To keep it clear, lets discuss simple square and cubes first.
 
The ratio of proportionality between two similar objects is the ratio between their linear dimensions: a = kb
 
If that figure is squared, the ratio of proportionality is similarly squared a2 = (kb)= k2b2 for the area
 
If that figure is cubed, the ratio of proportionality is similarly cubed a3 = (kb)3 = k3b3  for the volume
 
In this problem, we started with a ratio in volume of 3/4, this is the cube of ratio of proportionality.
So, k = ³√(3/4) = 0.9086  which is the linear ratio.
 
The area ratio will be k2 = (0.9086)2 = 0.8255
 
Further example
 
If I double the edges of the cube (k=2),
the surface area will increase by a factor of 4 (k= 22 = 4), and
the volume will increase by a factor of (k3= 23 = 8)
 
So, if someone had told me the volume of the food container was 8 times that of the water container, I would have concluded that the linear ratio of proportionality was 2, and that the ratio of surfaces areas was 22 = 4
 
 
 
This explanation was written for simple squares and cubes, but it applies to any two or three dimensional object.
 
la = klb, wa = kwb, ha = khb, ra = krb
 
Areas of Rectangles
lawa =k2lbwb
 
 
Volumes of Rectangular prisms
lawaha = k3lbwbhb
 
Areas of Circles 
πra2 = πk2rb2
 
Volumes of Spheres
(4/3)πra3 = (4/3)πk3rb3
 
 
 
and rectangular prisms
l= klb,  wa = kwb, h= khb  ⇒  lalblc =k3lbwbhb
 
 
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03/21/16

Elwyn D.

I just provided an extensive response to your question and it has not posted.  Forgive me but I do not have the energy to do it again.  I hope it does eventually post.
 
If the linear ratio of proportionality between two similar objects is k, then the ratio of proportionality between their areas will be kand the ratio of proportionality between their volumes will be k3.
 
This problem gave us k3 = (3/4) to start.
The cube root gave us k.
k2 gave us the ratio of their areas.
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03/21/16

Elwyn D.

Aha!  I read it wrong.  We were given the smaller surface area.  Correction posted above.
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03/21/16

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