the volume of a COMPOSITE / COMPOUND 3D FIGURE is 18 cm, 45 cm, 17 cm, and 20 cm

Question

The formula for volume of a PRISM is V=(area of the base) x (height of prism).
This prism is a composite figure with 2 prisms combined.
Find the volume of each prism separately then add the volumes together.
Part 1: Find the volume of the RECTANGULAR PRISM: __ YDS^3
Part 2: Find the volume of the TRIANGULAR PRISM: __ YDS^3
Part 3: Find the SUM of the volume of the 2 prisms: __ YDS^3

Answer 1

Part 1: Find the volume of the RECTANGULAR PRISM:

The formula for the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.

Given that the dimensions of the rectangular prism are 18 cm, 45 cm, and 17 cm:
V = 18 cm x 45 cm x 17 cm
V = 13770 cm^3

Converting the volume to cubic yards:
1 yard = 91.44 cm
1 yard^3 = (91.44 cm)^3 = 795,364.589 cm^3
13770 cm^3 / 795364.589 cm^3 = 0.0173 yard^3

Therefore, the volume of the RECTANGULAR PRISM is 0.0173 yard^3.

Part 2: Find the volume of the TRIANGULAR PRISM:

The formula for the volume of a triangular prism is V = 1/2 x b x h x l, where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism.

Given that the dimensions of the triangular prism are 18 cm, 17 cm (height), and 20 cm:
V = 1/2 x 18 cm x 17 cm x 20 cm
V = 3060 cm^3

Converting the volume to cubic yards:
3060 cm^3 / 795364.589 cm^3 = 0.0038 yard^3

Therefore, the volume of the TRIANGULAR PRISM is 0.0038 yard^3.

Part 3: Find the SUM of the volume of the 2 prisms:

Sum of the volumes = Volume of RECTANGULAR PRISM + Volume of TRIANGULAR PRISM
Sum of the volumes = 0.0173 yard^3 + 0.0038 yard^3
Sum of the volumes = 0.0211 yard^3

Therefore, the SUM of the volume of the 2 prisms is 0.0211 yard^3.