The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.
<h3>What is the Surface Area and Volume of Similar Shapes?</h3>
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.
Learn more about area and volume of similar shapes on:
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