Mean with Shapes Practice Test Worksheets
Mean with Shapes questions challenge you to work out the hidden numbers on a 3D shape based on the mean of all face values. This page shows how to count the faces, multiply to find the total sum, and solve for the missing values.
For students who understand basic average calculations, but need practice applying it to 3D spatial geometry puzzles.
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The Rules Every Mean with Shapes Question Uses
These puzzles use various 3D shapes. By identifying the shape and utilizing the mean, you can logically deduce the hidden values.
🔍 Rule 1: Count the total faces
Different shapes have different face counts. You must know the count to calculate the total sum.
Pyramids: 4 faces (triangle-based) or 5 faces (square-based). Cube: 6 faces.
📠 Rule 2: Find the total sum
Multiply the given mean by the number of faces to find the sum of all numbers on the shape.
Example: A 5-faced shape with a mean of 7 has a total sum of 35.
➕ Rule 3: Add visible faces
Sum up all the numbers displayed on the visible faces of the 3D diagram.
Note: Check if arrows point to bases or hidden sides to find all visible values.
➖ Rule 4: Find the hidden total
Subtract the visible sum from the total sum. The options must add to this hidden total.
Example: Total 35 − Visible 23 = 12. The correct option must be the one whose numbers add up to 12 (for example, 2 and 10).
3 Worked Examples
One straightforward pyramid, one prism, and one classic trap cube.
Question: The mean of the numbers on the faces of the triangle-based pyramid shown is 6. What are the two hidden numbers?
Options:
- A. 6 and 7
- B. 6 and 10
- C. 6 and 15
- D. 15 and 16
- E. 1 and 8
Worked Method
Step 1: Identify the shape. A triangle-based pyramid has 4 faces.
Step 2: Find the total sum. The mean is 6, so: 4 × 6 = 24.
Step 3: Add the visible numbers: 1 + 2 = 3.
Step 4: Find the hidden total: 24 − 3 = 21.
Step 5: Match to the options. Only 6 and 15 add to 21.
Answer: 6 and 15 → C.
Tip: Pay close attention to the shape's base type. A triangle-based pyramid has 1 base + 3 sides = 4 faces total.
Question: The mean of the numbers on the faces of the triangular prism shown is 5. What are the two hidden numbers?
Options:
- A. 1 and 9
- B. 5 and 8
- C. 2 and 6
- D. 6 and 9
- E. 3 and 6
Worked Method
Step 1: Identify the shape. A triangular prism has 2 triangular bases + 3 rectangular sides = 5 faces.
Step 2: Find the total sum. The mean is 5, so: 5 × 5 = 25.
Step 3: Add the visible numbers: 1 + 2 + 9 = 12.
Step 4: Find the hidden total: 25 − 12 = 13.
Step 5: Match to the options. Only 5 and 8 add to 13.
Answer: 5 and 8 → B.
Tip: Keep prism face counts clear. A triangular prism has 5 faces, whereas a rectangular prism (like a cuboid) has 6 faces.
Question: The mean of the numbers on the faces of the cube shown is 5. What are the three hidden numbers?
Options:
- A. 1, 2 and 3
- B. 3, 6 and 7
- C. 4, 5 and 6
- D. 1, 4 and 7
- E. 2, 3 and 4
Worked Method
Step 1: Identify the shape. A cube has 6 faces.
Step 2: Find the total sum. The mean is 5, so: 6 × 5 = 30.
Step 3: Add the visible numbers: 6 + 8 + 10 = 24.
Step 4: Find the hidden total: 30 − 24 = 6.
Step 5: Match to the options. Only 1, 2 and 3 add to 6.
Answer: 1, 2 and 3 → A.
Tip (The Trap): A common mistake is multiplying the mean by the number of visible faces (3) or assuming a 3D shape has 5 faces. Always multiply by the actual total faces of the geometric shape (6 for a cube).
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Mean with Shapes pack contains 90 questions across 3 printable test sets. Students practice average calculations across cubes, prisms, and pyramids with full answer keys included.
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