Answer:
The ratio of the volume of the triangular prism to the volume of the cuboid is 3: 20
Step-by-step explanation:
The volume of the triangular prism V[tex]_{T}[/tex] = [tex]\frac{1}{2}[/tex] bh × H, where
- b and h are the base and the height of the triangular base
- H is the height of the prism
The volume of the cuboid V[tex]_{C}[/tex] = L × W × H, where
- L and W are the dimensions of the base
- H is the height of the cuboid
∵ The base of the triangular prime is a right triangle with legs 5 cm, 4 cm
∴ b = 5 cm and h = 4 cm
∵ Its height is 9 cm
∴ H = 9 cm
→ Substitute them in the rule of the prism above
∵ V[tex]_{T}[/tex] = [tex]\frac{1}{2}[/tex] (5)(4) × 9
∴ V[tex]_{T}[/tex] = 90 cm³
∵ The dimensions of the base of the cuboid are 6 cm and 5 cm
∴ L = 6 cm and W = 5 cm
∵ Its height is 20 cm
∴ H = 20 cm
→ Substitute them in the rule of the cuboid above
∵ V[tex]_{C}[/tex] = 6 × 5 × 20
∴ V[tex]_{C}[/tex] = 600 cm³
→ Find the ratio between them
∵ V[tex]_{T}[/tex]: V[tex]_{C}[/tex] = 90: 600
→ Divide each term of the ratio by 30 to simplify them
∴ V[tex]_{T}[/tex]: V[tex]_{C}[/tex] = 3: 20
∴ The ratio of the volume of the triangular prism to the volume of
the cuboid is 3: 20
