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📦 Rectangular Prism Surface Area & Volume Lab

Unfold a box
and check surface area and volume

Change the width, depth, and height with sliders and see how a rectangular prism's surface area (the sum of all six faces) and volume change.

How much paint would you need to cover a delivery box completely? That's the surface area. A rectangular prism has three pairs of faces — top-bottom, front-back, side-side — and opposite faces are the same size. So finding three areas (width×depth, width×height, depth×height), adding them, and doubling the sum gives the surface area.

On the other hand, how much can fit inside the box is answered by volume. Volume is width×depth×height, the same as the number of unit blocks you'd need to fill the floor and stack them up to the height. Interestingly, doubling the width, depth, and height all at once multiplies the surface area by 4 (squared) and the volume by 8 (cubed).

Change one side at a time with the sliders and see for yourself how surface area and volume change at different rates.

Width (a)4
Depth (b)3
Height (h)2
Surface area
52
Volume
24