Volume of a Prism Textbook Exercise - Corbettmaths - Free Printable

Let’s solve each prism volume step by step.

Remember:
Volume of a prism = Area of the cross-section (base) × Length (or height, depending on orientation)

We’ll go one by one.

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(a) Rectangular prism
Base is rectangle: 3cm × 4cm → area = 12 cm²
Length = 6cm
Volume = 12 × 6 = 72 cm³

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(b) Triangular prism
Cross-section is right triangle: base 6cm, height 5cm
Area of triangle = (6 × 5)/2 = 15 cm²
Length = 20cm
Volume = 15 × 20 = 300 cm³

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(c) Triangular prism
Triangle base = 7m, height = 5m
Area = (7 × 5)/2 = 17.5 m²
Length = 4m
Volume = 17.5 × 4 = 70 m³

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(d) Rectangular prism — but units are mixed!
Dimensions: 1.1m, 2m, and 40cm → convert all to same unit. Let’s use meters.
40cm = 0.4m
So dimensions: 1.1m × 2m × 0.4m
Volume = 1.1 × 2 × 0.4 = 2.2 × 0.4 = 0.88 m³

*(Alternatively, if you used cm: 110cm × 200cm × 40cm = 880,000 cm³ = 0.88 m³ — same answer)*

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(e) Triangular prism
Triangle base = 7cm, height = 8cm (the dotted line shows perpendicular height)
Area = (7 × 8)/2 = 28 cm²
Length = 5.5cm
Volume = 28 × 5.5 = let’s calculate:
28 × 5 = 140, 28 × 0.5 = 14 → total = 154 cm³

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(f) Parallelogram-based prism
Base is parallelogram: base = 9cm, height = 6cm (perpendicular height shown)
Area = base × height = 9 × 6 = 54 cm²
Length = 12cm
Volume = 54 × 12 = 648 cm³
(54×10=540, 54×2=108 → 540+108=648) → 648 cm³

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(g) Right triangular prism
Triangle legs: 12cm and ? Wait — we have hypotenuse 13cm and one leg 12cm. Use Pythagoras to find other leg.

Let’s call unknown leg “x”:
x² + 12² = 13²
x² + 144 = 169
x² = 25 → x = 5cm

So triangle area = (12 × 5)/2 = 30 cm²
Length = 22cm
Volume = 30 × 22 = 660 cm³

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(h) Trapezoidal prism? Wait — looking at diagram: it's a prism with trapezoid cross-section? Actually, no — looks like a parallelogram again? Wait — labels: 40cm length, 10cm width, 8cm height (dotted). The base is a parallelogram: base 10cm, height 8cm.

Actually, rechecking: the figure has arrows showing 10cm as base, 8cm as perpendicular height, and 40cm as length.

So area of base (parallelogram) = 10 × 8 = 80 cm²
Volume = 80 × 40 = 3200 cm³

Wait — but there’s also “40cm” labeled along the side — yes, that’s the length. So correct.

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(i) Triangular prism
Triangle base = 11cm, height = 9cm
Area = (11 × 9)/2 = 99/2 = 49.5 cm²
Length = 15cm
Volume = 49.5 × 15
Calculate: 50 × 15 = 750, minus 0.5×15=7.5 → 750 - 7.5 = 742.5 cm³

Or: 49.5 × 10 = 495, 49.5 × 5 = 247.5 → 495 + 247.5 = 742.5 → same.

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Now double-checking all:

(a) 3×4×6 = 72 ✔️
(b) (6×5/2)×20 = 15×20=300 ✔️
(c) (7×5/2)×4 = 17.5×4=70 ✔️
(d) 1.1×2×0.4 = 0.88 ✔️
(e) (7×8/2)×5.5 = 28×5.5=154 ✔️
(f) 9×6×12 = 54×12=648 ✔️
(g) Found missing side 5cm → (12×5/2)×22 = 30×22=660 ✔️
(h) 10×8×40 = 80×40=3200 ✔️
(i) (11×9/2)×15 = 49.5×15=742.5 ✔️

All checked.

Final Answer:
(a) 72 cm³
(b) 300 cm³
(c) 70 m³
(d) 0.88 m³
(e) 154 cm³
(f) 648 cm³
(g) 660 cm³
(h) 3200 cm³
(i) 742.5 cm³