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Calculate the volume of each prism using the given dimensions.

A diagram showing nine different prisms with labeled dimensions for calculating volume, including rectangular, triangular, and parallelogram-based prisms.

A diagram showing nine different prisms with labeled dimensions for calculating volume, including rectangular, triangular, and parallelogram-based prisms.

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Show Answer Key & Explanations Step-by-step solution for: Y9. Shape & Space. Volumes of Prisms & Cylinders - Maths with David
Let’s solve each prism volume step by step.
Remember: Volume of a prism = Area of the base × height (or length) of the prism.

We’ll go one by one.

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

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(b) Triangular prism
Base is right triangle: base=6cm, height=5cm → area = (6×5)/2 = 15 cm²
Length = 20cm
Volume = 15 × 20 = 300 cm³

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(c) Triangular prism
Base 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, 40cm, 2m
Convert all to meters: 40cm = 0.4m
So dimensions: 1.1m × 0.4m × 2m
Volume = 1.1 × 0.4 × 2 = 0.88 m³
Or in cm: 110cm × 40cm × 200cm = 880,000 cm³ — but since question didn’t specify unit, we’ll use m³ as given for two sides.
Actually, better to convert everything to same unit. Let’s do cm:

1.1m = 110cm
2m = 200cm
40cm stays
Volume = 110 × 40 × 200 = 880,000 cm³
But maybe they expect m³? Let’s check: 1.1 × 0.4 × 2 = 0.88 m³
Either is correct, but since two measurements are in meters, let’s go with 0.88 m³

Wait — actually, looking at other problems, some mix units. But for consistency, perhaps we should pick one. Since 40cm is written as “40cm”, and others are “m”, it’s safer to convert all to cm.

1.1m = 110cm
2m = 200cm
40cm = 40cm
Volume = 110 × 40 × 200 = 880,000 cm³

But that seems huge. Alternatively, maybe they want answer in m³? Let’s see: 1.1 × 0.4 × 2 = 0.88 m³ — this is cleaner.

I think the problem expects us to handle unit conversion. So I’ll go with 0.88 m³

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(e) Trapezoidal prism? Wait — looks like a triangular prism again? Actually, no — it’s a prism with trapezoid base? Wait, no — looking at diagram: it has a vertical height of 8cm, base 7cm, and slant side 5.5cm — but actually, if it’s a prism, the cross-section is a triangle? Wait, no — the shape shown is a wedge — actually, it’s a triangular prism where the triangular face has base 7cm and height 8cm? But then why is there a 5.5cm? That might be the length of the prism.

Wait — re-examining: The figure shows a 3D shape with a triangular front face? No — actually, it looks like a prism whose base is a triangle with base 7cm and height 8cm, and the length (depth) is 5.5cm.

Yes — so area of triangle = (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

So 154 cm³

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(f) Parallelogram-based prism
Base is parallelogram: base=9cm, height=6cm → area = 9 × 6 = 54 cm²
Length = 12cm
Volume = 54 × 12 = 648 cm³

648 cm³

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(g) Right triangular prism
Triangle legs: 5cm and 12cm (right angle marked) → area = (5×12)/2 = 30 cm²
Length = 22cm
Volume = 30 × 22 = 660 cm³

Note: 13cm is hypotenuse — not needed for area.

660 cm³

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(h) Trapezoidal prism
Base is trapezoid: parallel sides 25cm and ? Wait — diagram shows bottom base 25cm, top base? It says 8cm? Wait — no: the red dashed line is height 8cm, and the two parallel sides are 25cm and... wait, actually, looking: it says "8cm" with arrow pointing to the top edge? And "25cm" at bottom. Also, the non-parallel sides are 10cm and 40cm? Wait — no, 40cm is the length of the prism.

Actually, standard interpretation: the cross-section is a trapezoid with:

- Parallel sides: let’s say a = 25cm, b = ? The diagram shows an arrow labeled "8cm" vertically — that’s the height of the trapezoid. But what is the top base? It doesn't say directly. Wait — look: there's a label "8cm" with a horizontal arrow on the top? Or is that the height?

Re-read: In (h), it says:
- Bottom base: 25cm
- Height of trapezoid: 8cm (red dashed line)
- Top base: ? Not labeled explicitly. But there's a label "8cm" with a horizontal arrow above — probably meaning the top base is 8cm? Yes, that makes sense.

Also, the length of the prism is 40cm (given on the side).

So trapezoid area = (sum of parallel sides)/2 × height = (25 + 8)/2 × 8 = (33/2) × 8 = 16.5 × 8 = 132 cm²

Then volume = 132 × 40 = 5280 cm³

5280 cm³

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(i) Triangular prism
Base triangle: base=14cm, height=9cm → area = (14×9)/2 = 63 cm²
Length = 15cm
Volume = 63 × 15 = 945 cm³

Note: 11cm is a side — not needed.

945 cm³

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Now, let’s list all answers clearly:

(a) 72 cm³
(b) 300 cm³
(c) 70 m³
(d) 0.88 m³ (or 880,000 cm³ — but we'll use m³ as per dominant units)
(e) 154 cm³
(f) 648 cm³
(g) 660 cm³
(h) 5280 cm³
(i) 945 cm³

For (d), to be precise, since 40cm is given, and others in m, converting to consistent units is best. But in many textbooks, they accept either as long as units are correct. However, 0.88 m³ is simpler.

Alternatively, let’s double-check (d):
1.1m × 40cm × 2m
Convert 40cm to 0.4m → 1.1 × 0.4 × 2 = 0.88 m³ — yes.

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) 5280 cm³
(i) 945 cm³
Parent Tip: Review the logic above to help your child master the concept of volume of prisms and cylinders worksheet answers.
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