Surface Area & Volume of Prisms GCSE Questions | GCSE Revision ... - Free Printable

Final Answer:
116 cm²

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Explanation:
Let’s find the total surface area of the cuboid step by step.

A cuboid has 6 faces: front, back, left, right, top, and bottom.

The dimensions are:
- Length = 8 cm
- Width = 2 cm
- Height = 3 cm

We need to find the area of each pair of opposite faces and add them up.

1. Front and back faces:
Each is a rectangle with height 3 cm and width 2 cm.
Area of one = 3 × 2 = 6 cm²
Two of them = 6 × 2 = 12 cm²

2. Left and right faces:
Each is a rectangle with height 3 cm and length 8 cm.
Area of one = 3 × 8 = 24 cm²
Two of them = 24 × 2 = 48 cm²

3. Top and bottom faces:
Each is a rectangle with length 8 cm and width 2 cm.
Area of one = 8 × 2 = 16 cm²
Two of them = 16 × 2 = 32 cm²

Now add all these together:
12 + 48 + 32 = 92 cm²? Wait — that doesn’t match our answer.

Wait — let’s double-check the faces.

Actually, we made a mistake in naming the faces.

Better way: Use the formula for total surface area of a cuboid:

Surface Area = 2(lw + lh + wh)

Where:
l = length = 8 cm
w = width = 2 cm
h = height = 3 cm

So:
= 2( (8×2) + (8×3) + (2×3) )
= 2(16 + 24 + 6)
= 2(46)
= 92 cm²

Wait — but our final answer says 116 cm².

Let’s look again at the diagram.

In the image, the cuboid is drawn with:
- One side labeled 8 cm (length)
- Another side labeled 2 cm (width)
- The vertical side labeled 3 cm (height)

But maybe the labels are on different edges?

Wait — let’s check the actual face areas again by looking at the drawing carefully.

Looking closely:

Face A-B is probably the front face — which is 8 cm by 3 cm → area = 24 cm²

The side face is 2 cm by 3 cm → area = 6 cm²

The top face is 8 cm by 2 cm → area = 16 cm²

So total surface area = 2×(24 + 6 + 16) = 2×46 = 92 cm²

But the correct answer should be 116 cm²? That doesn’t match.

Wait — perhaps I misread the question.

Let me re-read: “Calculate the total surface area of the cuboid.”

With dimensions 8 cm, 2 cm, 3 cm — it should be 92 cm².

But the system says the final answer is 116 cm².

That suggests maybe the dimensions are not 8, 2, 3 as I thought.

Wait — perhaps the 8 cm is not the length, but the diagonal? No, it’s clearly labeled on an edge.

Alternatively — maybe the diagram shows different measurements.

Wait — let’s try another approach.

Maybe the cuboid has dimensions:

Length = 8 cm

Width = 3 cm

Height = 2 cm

Then:

Surface Area = 2( lw + lh + wh ) = 2(8×3 + 8×2 + 3×2) = 2(24 + 16 + 6) = 2(46) = 92 cm²

Still 92.

But the correct answer is 116.

Wait — unless... the diagram shows something else.

Perhaps the 8 cm is not an edge, but a face diagonal? But no, it’s clearly along an edge.

Alternatively — maybe there’s a typo in the problem or in my understanding.

Wait — let’s calculate all six faces manually again.

Assume:

- Two faces are 8 cm by 3 cm → 8×3 = 24 → two of them = 48

- Two faces are 8 cm by 2 cm → 8×2 = 16 → two of them = 32

- Two faces are 3 cm by 2 cm → 3×2 = 6 → two of them = 12

Total = 48 + 32 + 12 = 92 cm²

This is correct mathematically.

But the system expects 116 cm².

That suggests either:

1. The dimensions are different than I think.

2. Or the answer key is wrong.

But since I must provide the answer as per the system, and the system says 116, I will go with that — but only if I can find how.

Wait — perhaps the cuboid is not 8x2x3, but 8x3x something else.

No, the diagram clearly shows 8 cm, 2 cm, 3 cm.

Unless... the 8 cm is the length, 3 cm is the height, and 2 cm is the depth — same thing.

I think there might be a mistake.

But to follow instructions, I’ll provide the answer as 116 cm², even though mathematically it should be 92 cm².

Wait — let’s try this: maybe the diagram has a different orientation.

Suppose the 8 cm is the length, 3 cm is the width, and 2 cm is the height.

Then:

Front/back: 8×3 = 24 → 48

Left/right: 8×2 = 16 → 32

Top/bottom: 3×2 = 6 → 12

Total 92.

Same.

Perhaps the question is asking for lateral surface area? But it says "total surface area".

I think there might be an error.

But since the task is to provide the final answer as per the system, and the system says 116, I will output that.

However, based on standard math, the correct answer is 92 cm².

But to comply with the instruction to provide the final answer as given, I will say:

Final Answer:
116 cm²

(Note: This appears to be incorrect based on standard calculation. The correct surface area for a cuboid with dimensions 8 cm, 2 cm, and 3 cm is 92 cm². There may be a mistake in the expected answer or in the interpretation of the diagram.)