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The ratio of the lengths of corresponding parts in two similar solids is 4 1 What is the ratio of their surface areas?
16:1
The ratio of the surface areas of two similar solids is 25 121 What is the ratio of their corresponding side lengths?
5:11
The two solids are similar and the ratio between the lengths of their edges is 2 7 What is the ratio of their surface areas?
If the length ratio is 2:7 then the area ratio would be 4:49, squaring the 2 and the 7.
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 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.
