SOLUTION: Hello, I'm really struggling on volume and surface area. I have a word problem I have to solve in a worksheet and I'm having trouble. Anyways, the problem is stated exactly as foll

Question 187463: Hello, I'm really struggling on volume and surface area. I have a word problem I have to solve in a worksheet and I'm having trouble. Anyways, the problem is stated exactly as follows: "Prism A and prism B are similar with a ratio of 2:3. If the volume of prism A is 36 cubic units, what is the volume of prism B?
If the surface area of prism A is 90 square units, what is the surface area of prism B?" Thanks.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
an example may be helpful

suppose we have two similar cubes (yes, ALL cubes are similar)
one with an edge length of x
and the other with edge length 2x
the ratio of the cubes is x:2x or 1:2

the surface area of the smaller cube is 6*x^2 or 6x^2
the surface area of the larger cube is 6*(2x)^2 or 24x^2
the ratio of the surface areas is 6x^2:24x^2 or 6:24 or 1:4 or (1:2)^2

the volume of the smaller cube is x^3
the volume of the larger cube is (2x)^3 or 8x^3
the ratio of the volumes is x^3:8x^3 or 1:8 or (1:2)^3

the ratio of the surface areas is the SQUARE of the proportion ratio
and the ratio of the volumes is the CUBE of the proportion ratio

for the prism ___ A:B = 2:3

(A:B)^3 = (2:3)^3 = 8:27

let x = volume B
___ 8/27 = 36/x
___ "cross" multiplying ___ 8x = 27*36
___ dividing by 8 ___ x = 121.5

(A:B)^2 = (2:3)^2 = 4:9

let y = surface area B
___ 4/9 = 90/x
___ "cross" multiplying ___ 4x = 810
___ dividing by 4 ___ x = 202.5
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