Students understand that given similar solids 𝐴 and 𝐵 so that the ratio of their lengths is 𝑎: 𝑏, then the ratio of their volumes is 𝑎 3 : 𝑏 3 .
Students understand that if a solid with volume 𝑉 is scaled by factors of 𝑟, 𝑠, and 𝑡 in three perpendicular directions, then the volume is multiplied by a factor of 𝑟 ⋅ 𝑠 ⋅ 𝑡 so that the volume of the scaled solid is (𝑟𝑠𝑡)
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