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If the sides of two shapes are in the ratio of A : B, then their volumes are in the ratio A3 : B3, thus:

ratio of volumes = 125 : 9

ratio of sides = 3√125 : 3√9 ~= 5: 2.08

(~= 2.4 : 1)

Have you got the volumes correct?

I suspect the second should be 8cm3 not 9cm3, because then the volumes would be 125cm3 and 8cm3 and:

ration of volumes = 125 : 8

ratio of sides = 3√125 : 3√8

= 5 : 2

(= 2.5 : 1)

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Q: If two similar prisms have volumes of 125 cm3 and 9 cm3 what is the side ratio of the two prisms?

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If the ratio of side lengths is 49 (that is 49 to 1) then the ratio of their volumes is 493 to 1, which is 117,649 to 1.

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Cubes have a square on each side, but rectangular prisms have rectangles or squares.

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If the ratio of side lengths is 49 (that is 49 to 1) then the ratio of their volumes is 493 to 1, which is 117,649 to 1.

area = side x side if the side is halved, then new_area = side/2 x side/2 = side x side / 4 = area / 4 The area becomes a quarter of what is was. With similar objects, The ratio of areas is the square of the ratio of the lengths The ratio of volumes is the cube of the ratio of the lengths.

Their perimeters are in the same ratio.

If you are trying to find the ratio of the lengths of two similar rectangles, divide the length of one side of one rectangle by the corresponding side length of the other rectangle. To find the ratio between their volumes, divide the volume of one rectangle by the volume the other rectangle. To find volume, multiply the width of the rectangle by the length of the rectangle.

It is the same.

7:10

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Cubes have a square on each side, but rectangular prisms have rectangles or squares.

7:10

5:11

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