GeometryFormula

Rectangular Prism Practice Problems

15 rectangular prism problems with full worked solutions, graded from warm-up to stretch — plus an unlimited supply you can generate yourself. Every answer is computed by the same verified function that powers the rectangular prism explorer, so the solutions cannot disagree with the formulas. Free, no account, nothing to install.

Formulas you need

  • Volume: V=lwhV = l w h
  • Surface area: SA=2(lw+lh+wh)SA = 2(lw + lh + wh)
  • Space diagonal: d=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}

where l, w, h = length, width, height, V = volume, SA = surface area

Generate a new problem

Pick a difficulty, work it out, then check your answer. Every press gives a new question — the numbers are drawn fresh each time, so you can keep going.

Warm-up

  1. A rectangular prism has length l = 4, width w = 1 and height h = 2. Find the volume (V).

    Answer & working

    8 units³

    V = l · w · h = 4 · 1 · 2 = 8

  2. A rectangular prism has length l = 1, width w = 3 and height h = 5. Find the surface area (SA).

    Answer & working

    46 units²

    SA = 2(lw + lh + wh) = 2(3 + 5 + 15) = 46

  3. A rectangular prism has length l = 1, width w = 5 and height h = 5. Find the space diagonal (d).

    Answer & working

    7.14 units

    diagonal = √(l²+w²+h²) ≈ 7.14

  4. A rectangular prism has length l = 5, width w = 5 and height h = 2. Find the volume (V).

    Answer & working

    50 units³

    V = l · w · h = 5 · 5 · 2 = 50

  5. A rectangular prism has length l = 2, width w = 3 and height h = 1. Find the surface area (SA).

    Answer & working

    22 units²

    SA = 2(lw + lh + wh) = 2(6 + 2 + 3) = 22

Core practice

  1. A rectangular prism has length l = 1, width w = 1 and height h = 9. Find the volume (V).

    Answer & working

    9 units³

    V = l · w · h = 1 · 1 · 9 = 9

  2. A rectangular prism has length l = 9, width w = 7 and height h = 10. Find the surface area (SA).

    Answer & working

    446 units²

    SA = 2(lw + lh + wh) = 2(63 + 90 + 70) = 446

  3. A rectangular prism has length l = 7, width w = 8 and height h = 10. Find the space diagonal (d).

    Answer & working

    14.59 units

    diagonal = √(l²+w²+h²) ≈ 14.59

  4. A rectangular prism has length l = 6, width w = 8 and height h = 8. Find the volume (V).

    Answer & working

    384 units³

    V = l · w · h = 6 · 8 · 8 = 384

  5. A rectangular prism has length l = 8, width w = 6 and height h = 9. Find the surface area (SA).

    Answer & working

    348 units²

    SA = 2(lw + lh + wh) = 2(48 + 72 + 54) = 348

Stretch

  1. A rectangular prism has length l = 7.5, width w = 10 and height h = 1.5. Find the volume (V).

    Answer & working

    112.5 units³

    V = l · w · h = 7.5 · 10 · 1.5 = 112.5

  2. A rectangular prism has length l = 1.5, width w = 6.5 and height h = 8.5. Find the surface area (SA).

    Answer & working

    155.5 units²

    SA = 2(lw + lh + wh) = 2(9.75 + 12.75 + 55.25) = 155.5

  3. A rectangular prism has length l = 1.5, width w = 10 and height h = 5.5. Find the space diagonal (d).

    Answer & working

    11.51 units

    diagonal = √(l²+w²+h²) ≈ 11.51

  4. A rectangular prism has length l = 1.5, width w = 1.5 and height h = 7.5. Find the volume (V).

    Answer & working

    16.88 units³

    V = l · w · h = 1.5 · 1.5 · 7.5 ≈ 16.88

  5. A rectangular prism has length l = 5.5, width w = 8.5 and height h = 6.5. Find the surface area (SA).

    Answer & working

    275.5 units²

    SA = 2(lw + lh + wh) = 2(46.75 + 35.75 + 55.25) = 275.5

Answers are recomputed from the verified rectangular prism function every time this page is built, and every printed line is checked to evaluate correctly. Content last reviewed August 2026. Found a mistake? Tell us — we correct and republish.

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