The composite figure is a combination of a rectangular pyramid and a rectangular prism, hence its volume is 140in³.
Rectangular Prism and Pyramid
A rectangular prism is simply a three dimensional solid shape with six faces that are rectangles.
Volume of a rectangular prism is expressed as;
V = w × h × l
Where l is length, h is height and w is width
A rectangular pyramid is simply a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.
The volume of rectangular pyramid is expressed as;
V = (1/3) × l × w × h
Where l is the base length, w is the base width and h is the height of the pyramid.
From the diagram below;
- Length of rectangular prism Lprism = 7in
- Width of rectangular prism Wprism = 3in
- Height of rectangular prism Hprism = 4in
- Length of rectangular pyramid Lpyramid = 7in
- Width of rectangular pyramid Wpyramid = 3in
- Height of rectangular pyramid Hpyramid = 12in - 4in = 8in
First we calculate the volume of a rectangular prism.
V = w × h × l
V = 3in × 4in × 7in
V = 84in³
Hence, the volume of the rectangular prism is 84in³.
Next, we calculate the volume of rectangular pyramid.
V = (1/3) × l × w × h
V = (1/3) × 7in × 3in × 8in
V = (1/3) × 168in³
V = 56in³
Hence, the volume of the rectangular pyramid is 56in³.
Volume of the composite figure = Volume of prism + Volume of pyramid
Volume of the composite figure = 84in³ + 56in³
Volume of the composite figure = 140in³
Therefore, the composite figure is a combination of a rectangular pyramid and rectangular prism, hence its volume is 140in³.
Learn more about volume of pyramids here: brainly.com/question/21308574
