Answer to Question #168646 in Geometry for Adam

Question #168646

Solid A and solid B are similar. The surface area of solid A is 675 m2 and the surface area of solid B is 432 m2. If the volume of solid B is 960 m3, find the volume of solid A.


1
Expert's answer
2021-03-09T12:38:11-0500

Answer


  • As the shape of solids are not given, lets start from the definition of the volume: "\\small V=L\\times W\\times H"

"\\qquad\\qquad\n\\begin{aligned}\n\\small V_b&= \\small L_b\\times W_b\\times H_b\\\\\n\\small V_a&= \\small L_a\\times W_a\\times H_a\n\\end{aligned}"

  • Since the solids are similar,

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\frac{Area_a}{Area_b}&= \\small (\\frac{L_a}{L_b})^2=(\\frac{W_a}{W_b})^2=(\\frac{H_a}{H_b})^2\\\\\n\\small \\frac{675}{432}=(\\frac{5}{4})^2&= \\small \\small (\\frac{L_a}{L_b})^2=(\\frac{W_a}{W_b})^2=(\\frac{H_a}{H_b})^2\\\\\n\\\\\nThen,\\\\\n\\\\\n\\small L_a&= \\small \\frac{5L_b}{4}\\\\\n\\small W_a&= \\small \\frac{5W_b}{4}\\\\\n\\small H_a&= \\small \\frac{5H_b}{4}\\\\\n\\\\\n\n\\therefore\\small V_a&= \\small \\frac{5L_b}{4}\\times \\frac{5W_b}{4}\\times \\frac{5H_b}{4}\\\\\n&= \\small (\\frac{5}{4})^3\\times V_b\\\\\n&= \\small 1875m^3\n\n\n\\end{aligned}"


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