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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.

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akposevictor

The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.

What is the Surface Area and Volume of Similar Shapes?

If two solids, A and B, are given and have corresponding dimensions as a and b respectively, we would have the following:

Surface area of solid A/Surface area of solid B = a²/b²

Volume of solid A/Volume of solid B = a³/b³

Given that solid A and solid B are similar, and:

  • Surface area of solid A = 675 m²
  • Surface area of solid B = 432 m²
  • Volume of solid B = 960 m³.

Find their corresponding dimensions, a and b:

Surface area of solid A/Surface area of solid B = a²/b²

Substitute

675/432 = a²/b²

√(675/432) = a/b

1.25 = a/b

Scale factor of Solid A to Solid B is 1.25.

Multiply 1.25 by 960 to get the volume of solid A.

Volume of solid A = 960 × 1.25 = 1,200 m³.

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