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The two solids below are similar and the ratio between the lengths of their edges is 35. What is the ratio of their surface areas?
If the lengths are in the ratio 3:5, then the surface areas are in the ratio 9:25.
What is the ratio for the volumes of two similar spheres given that the ratio of their radii is 27?
If the ratio is 2 : 7 then the volumes are in the ratio 8 : 343.
How is the ratio of the volumes related to the ratio of corresponding dimensions?
The answer depends on whether or not the shapes are similar. If they are, then the ratio of volumes is the cube of the ratio of the linear dimensions.
Describe what happens to the surface area to volume ratio for larger and larger cubes?
For a cube with edge length, L. Surface area = 6L2. Volume = L3. So ratio of Surface Area / Volume = 6 / L. Therefore, as the side length, L, increases, the ratio will decrease.
If two solids are similar and the ratio between their lengths is 2 9 what is the ratio of their surface areas?
The ratio of area is 4 : 81.
How the ratio of volume is related to ratio of sides of similar cubes?
The ratio of volumes is directly proportional to the cube of the ratio of their sides. And, incidentally, all cubes are similar.
If the edges of two cubes are in the ratio 2 to 3 then what is the ratio of their volumes?
(2/3)3 = 8/27
Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism. How are the surface areas of the figures related?
The ratios of areas are the squares of the ratio of lengths (and the ratio of volumes are cubes of the ratio of lengths). As the perimeter of the second is twice the perimeter of the first, each length of the second is twice the length of the first, and so the ratio of the lengths is 1:2 Thus the ratio of the areas is 1²:2² = 1:4. Therefore the surface area of the larger prism is four times that of the smaller prism.
The volumes of two similar figures are 512 mm3 and 3375mm3. If the surface area of the smaller figure is 128mm2. What is the surface area of the larger figure?
450 mm2 Ratio of areas is the square of the ratio of lengths. Ratio of volumes is the cube of the ratios of lengths. If the volumes are in the ratio of 512 to 3375, then the lengths are in the ratio of: 3√512 : 3√3375 = 8 : 15 ⇒ ratios of areas: 82 : 152 = 64 : 225 ⇒ as smaller has surface area of 128 mm2, the larger has: surface_area = (128 ÷ 64) x 225 mm2 = 450 mm2
How do you calculate surface area to volume ratio?
You measure or calculate the surface area; you measure or calculate the volume and then you divide the first by the second. The surface areas and volumes will, obviously, depend on the shape.
The diameter of the moon is approximately one fourth of the diameter of the earth find the ratio of their surface areas?
The ratio of the surface areas of two similar objects is equal to the square of the ratio of their corresponding linear dimensions. Since the diameter of the moon is one fourth of the diameter of the Earth, the ratio of their diameters is 1:4. Therefore, the ratio of their surface areas is (1/4)^2 = 1/16. This means that the surface area of the moon is 1/16th of the surface area of the Earth.
The ratio of the lengths of corresponding parts in two similar solids is 4 1 what is the ratio of their surface areas-?
The ratio of their surface areas is the square of the ratio of the lengths. Since the ratio of the lengths is 4-1, then the ratio of the surface areas is 4^2-1^2 or 16-1.
How do you find the ratio of two similar 3 dimensional figures when only given the surface area?
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
The two solids below are similar and the ratio between the lengths of their edges is 35. What is the ratio of their surface areas?
If the lengths are in the ratio 3:5, then the surface areas are in the ratio 9:25.
The ratio of the corrresponding edge lengths of two similar soilds is 4 5 what is the ratio of their surface areas?
The ratio of their surface areas is 42 to 52 or 16 to 25
What is the ratio for the volumes of two similar pyramids given that the ratio of their edge lengths is 5 to 7?
The ratio is 57 cubed. This answer does not depend on the fact that you are comparing two similar pyramids; it works the same for two cubes, two spheres, etc. - in general, for any two similar 3D objects.
What is the ratio of the height of two similar cones with a surface area ratio of 4 over twenty five?
Where objects are SIMILAR (scale versions of each other) then the ratio of linear measurements is a : b, the ratio of areas is a2 : b2 and the ratio of volumes is a3 : b3. As the area ratio is 4 : 25 = a2 : b2 = 22 : 52 then the ratio of their heights is a : b = 2 : 5.
