Question

Find the ratio of the volume of the triangular prism

Answer 1

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$_{T}$ = $\frac{1}{2}$ 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$_{C}$ = 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$_{T}$ = $\frac{1}{2}$ (5)(4) × 9

∴ V$_{T}$ = 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$_{C}$ = 6 × 5 × 20

∴ V$_{C}$ = 600 cm³

→ Find the ratio between them

∵ V$_{T}$: V$_{C}$ = 90: 600

→ Divide each term of the ratio by 30 to simplify them

∴ V$_{T}$: V$_{C}$ = 3: 20

∴ The ratio of the volume of the triangular prism to the volume of

   the cuboid is 3: 20