Question
The volumes of two similar solids are 1331 cubic meters and 27 cubic meters. The surface area of the larger one is 242 square meters. What is the surface area of the smaller one?
Answers
Reiny
the volumes of 2 similar solids are proportional to the cube of their corresponding sides
the surface ares of two similar solids are proportional to the square of their corresponding sides
so side1^3/side2^3 = 1331 / 27 = 11^3/3^3
side1/side2 = 11/3
area1/area2 = 11^2/3^2
242/area2 = 121/9
121area2 = 2178
area1 = 2178/121 = 18
the surface ares of two similar solids are proportional to the square of their corresponding sides
so side1^3/side2^3 = 1331 / 27 = 11^3/3^3
side1/side2 = 11/3
area1/area2 = 11^2/3^2
242/area2 = 121/9
121area2 = 2178
area1 = 2178/121 = 18