Question 971860: If you are given two similar rectangular prisms with a ratio of 1:3 where the volume of the smaller prism is 7 cubic feet and the surface area 30 square feet, what is the volume and surface area of the larger prism? Show your calculations and explain your thinking.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  = height of the small prism.
 = width of the base of the small prism.
 = length of the base of the small prism.
Why and not  ?
Because the letter  looks too much like the number and I do not want any confusion.
 = height of the large prism.
 = width of the base of the large prism.
 = length of the base of the large prism.
The volume of the prisms is calculated as
 = volume of the small prism, and
 = volume of the large prism.
Maybe you have been taught that
if the ratio of corresponding rates is  , then
 and  .
That is true for all similar shapes, not just rectangular prisms.
IF you have not been taught that it is true for rectangular prisms,
it is easy to prove it for this case, as shown below:
The total surface area of the prisms is calculated as
 = total surface area of the small prism, and
 = total surface area of the large prism.
Because the prisms are "two similar rectangular prisms with a ratio of 1:3"
 ,  and  , so
 and
 .
In this case,  and  , so
 and
 .
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