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The surface areas of two similar figures are given below. The volume of the smaller figure is also given. What is the volume of the larger figure?
Solid #1
SA= 8yd^2
V= 17yd^3
Solid #2
SA= 128yd^2
V= ?
Volume of the larger figure = ?yd^3
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The ratio of surface areas is = 16 (the larger to the smaller).
Hence, the ratio of linear dimensions is = 4.
It means that the ratio of volumes is 4^3 = 64.
Hence, the volume of the larger body is 64 times the volume of the smaller body, i.e.
V = 64*17*yd^2 = 1088yd^2. ANSWER
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