The figures below are similar.4 m8 mWhat is the ratio of the surface area of the smaller cylinder to the surface area of the larger cylinder?Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).
Question
The figures below are similar.4 m8 mWhat is the ratio of the surface area of the smaller cylinder to the surface area of the larger cylinder?Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).
Solution
The question seems to be missing the figures mentioned. However, if we assume that the figures are two cylinders and the numbers given (4m and 8m) are their respective heights or diameters, we can still find the ratio of their surface areas.
The surface area of a cylinder is given by the formula 2πr(h + r), where r is the radius and h is the height. If the cylinders are similar and the dimensions of the larger one are twice that of the smaller one, then the ratio of their surface areas is the square of the ratio of their corresponding lengths.
So, if the ratio of the heights (or diameters) of the two cylinders is 4:8 or 1:2, then the ratio of their surface areas will be (1:2)^2 = 1:4.
So, the ratio of the surface area of the smaller cylinder to the surface area of the larger cylinder is 1:4.
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