The volume of the joined prism is given by the sum of the volume of the
individual prisms.
Correct responses:
The rectangular prisms that could be joined to create a solid figure are;
- Figure 1 joined to figure 2 gives 44 cube units
- Figure 3 joined to figure 5 gives 46 cube units
Method used to find the volume of the combined prisms
The volumes of the given rectangular prisms are;
Volume of first prism, V₁ = 4 units × 4 units × 3 units = 36 cube units
Volume of second prism, V₂ = 4 units × 1 unit × 2 units = 8 cube units
Third prism, V₃ = 5 units × 3 units × 2 units = 30 cube units
Fourth prism, V₄ = 5 units × 4 units × 2 units = 40 cube units
Fifth prism, V₅ = 4 units × 2 units × 2 units = 16 cube units
V₁ + V₂ = 36 cube units + 8 cube units = 44 cube units
V₃ + V₅ = 30 + 16 = 46 cube units
Therefore the two rectangular prisms that could be joined to create a solid figure with a volume between 42 and 47 are;
- 1) The first and the second prisms
- 2 The third and the fifth prisms
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