if a cube is 6x6x6 if the side lengths are doubled what is the ratio of the original volume to the new volume wouldn't it be 1:8 because the original is 216 ft^3 and new is 1728 that ratio is 1:8?

Answer 1

Yes, it's 1:8. When you double the side lengths, the scale factor is k = 2. The surface area increases as k² = 2² = 4, so the larger cube has 4 times the surface area of the smaller one. The volume increases as k³ = 2³ = 8, so the larger cube has 8 times the volume of the smaller cube.