Question

©2018 Strong Mind

14 cm
What is the volume for the figure in cubic centimeters?
Enter your answer as a number, like this: 42
Do not enter units.
4 cm
8 cm
20 cm
2 cm

Answer 1

By decomposing the figure into a rectangular prism and a triangular prism, calculating their individual volumes, and adding them up, we found that the total volume of the figure is 304 cubic centimeters.

1. Identify and decompose the solid:

The figure is a combination of two basic solids:

A rectangular prism: This forms the base of the figure, with dimensions 8 cm (length) x 14 cm (width) x 2 cm (height).

A triangular prism: This sits on top of the rectangular prism, sharing the same 8 cm x 2 cm base. Its triangular face has dimensions 8 cm (base) and 20 cm (height).

2. Calculate the volume of each solid:

Rectangular prism volume:
`V_(prism )`= lwh = 8 cm x 14 cm x 2 cm = 224 cm³

Triangular prism volume:
`V_(prism)` = ½bh = ½ * 8 cm * 20 cm = 80 cm³

3. Calculate the total volume:

The total volume of the figure is the sum of the volumes of the two individual solids:

`V_(total) = V_(rectangular prism) + V_(triangular prism)` = 224 cm³ + 80 cm³ = 304 cm³

Therefore, the volume of the figure is 304 cubic centimeters.