Surface Area of 3D Shapes

Geometry · Axiom Academy

LESSON Surface Area of 3D Shapes Finding the total area covering a solid — the wrapping-paper view of geometry. 1. Surface Area Is the Area of the Net A net is a 2D pattern that folds up into a 3D shape. Unfold a cube and you get six identical squares ; unfold a cylinder and you get two circles plus a rectangle . Finding the surface area is just finding the total area of that flattened net. 6 identical squares — one for each face. 2 circles (top & bottom) + 1 rectangle (the side, unrolled). Every formula below is just " bases + lateral surface ". Watch the cylinder unroll: the curved side opens into a rectangle whose width is the circle's circumference, 2πr , and whose height is h — so its area is 2πr·h. Add the two circular caps (2·πr²) and you have the whole formula. Cylinder: two caps + the unrolled side Sum of the 6 rectangular faces. 4 times a great circle (all curved). Watch the 8×5×3 box unfold flat into its six rectangles. Each rectangle is labelled with its own area, and the areas add up — front/back, then top/bottom, then left/right — to the total in the readout. The area of the whole net is the surface area. Find the surface area of a box with length 8 cm, width 5 cm, and height 3 cm. A cone has radius 6 cm and slant height 10 cm. Find its total surface area. (Use π ≈ 3.14.) A basketball has diameter 24 cm. Find its surface area. (Use π ≈ 3.14.)

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