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Similar 3D shapes: length k, area k², volume k³

Choose a 3D solid (cuboid, cylinder or cone), rotate the 3D view by dragging, and adjust the scale factor k. Compare the actual surface areas and volumes of both shapes, or switch to Work backwards mode to find the length scale factor k = ∛(V₂ / V₁) from a given volume ratio.

3D solid:
Mode:
Drag to rotate both 3D solids together
k = 2.00 | k² = 4.00 | k³ = 8.00
Scale factor control
×2.00
Quick k:
Original Solid A dimensions (cm)

1. Scale factor rules (k → k² → k³)

Forward mode

2. Actual dimensions, surface areas & volumes

Cuboid

Both methods always agree: calculating the surface area and volume directly from Solid B's enlarged dimensions gives the exact same result as multiplying Solid A's values by k² and k³.