Visualising Solid Shapes Worksheet Page 8
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42M A T H E M A T I C S
Example 13 : A polyhedron has 7 faces and 10 vertices. How many
edges does the polyhedron have?
Solution
: For any polyhedron,
F + V – E = 2
Here, F = 7, V = 10, E = ?
Using above formula,
⇒7 + 10 – E = 2
⇒17 – E = 2
⇒17 – 2 = E
⇒ Ε = 15
Example 14 : Find the number of vertices in a polyhedron which has
30 edges and 12 faces.
Solution
: For any polyhedron,
F + V – E = 2
Here, F = 12, V = ?, E = 30
Using above formula,
12 + V – 30 = 2
V – 18 = 2
V = 2 + 18
V = 20
Example 15 : The distance between City A and City B on a map is
given as 6 cm. If the scale represents 1 cm = 200 km,
then find the actual distance between City A and City B.
Solution
: Actual distance represented by 1cm = 200 km
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What is the surface area of a single block in square units?
If the edge lengths of a block are 2 cm, what is the block’s surface area?
What is the volume of the structure at the right in cubic units?
What is the surface area of the structure above in square units?
(Remember: Count only the squares on the outside of the structure.)
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