How it works
For a rectangular box with dimensions l, w and h, there are three pairs of matching faces:
SA = 2(lw + lh + wh)
A cube with edge s has 6 equal faces, so SA = 6s². A cylinder has two circles plus a rectangle that wraps around the side, so SA = 2πr² + 2πrh = 2πr(r + h).
When solids are glued together face to face, each joint hides two faces (one from each solid). Find the total for the separate pieces and subtract the hidden faces.
Surface Area practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
A cube has volume 64. Find its surface area.
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Answer: 96
The edge is 4 because 4³ = 64. Each face has area 16, so SA = 6 × 16 = 96.
A rectangular prism measures 4 by 5 by h and has surface area 148. Find h.
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Answer: 6
2(20 + 4h + 5h) = 148, so 20 + 9h = 74, giving 9h = 54 and h = 6.
Three 2 by 2 by 2 cubes are glued in a row face to face. Find the surface area of the new solid.
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Answer: 56
Separately the cubes have 3 × 24 = 72. The two joints each hide 2 faces of area 4, which is 16 in total. 72 − 16 = 56.
A cylinder has radius 5, height 3. Total surface in terms of π?
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Answer: 80π
SA = 2πr(r + h) = 2π × 5 × 8 = 80π.
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