1. Find the volume of the following composite figure:
The figure consists of a rectangular prism with dimensions 6 cm x 4 cm x 8 cm, resting on top of a triangular prism with a base of 6 cm, height of 4 cm, and length of 8 cm.
First, find the volume of the rectangular prism:
Volume = length x width x height
Volume = 6 cm x 4 cm x 8 cm
Volume = 192 cm³
Next, find the volume of the triangular prism:
Volume = 1/2 x base x height x length
Volume = 1/2 x 6 cm x 4 cm x 8 cm
Volume = 96 cm³
Finally, add the volumes of the two prisms together to get the total volume of the composite figure:
Total volume = 192 cm³ + 96 cm³
Total volume = 288 cm³
Therefore, the volume of the composite figure is 288 cm³.
2. Find the volume of the following composite figure:
The figure consists of a cylinder with a radius of 5 cm and a height of 10 cm, intersecting a sphere with a radius of 5 cm.
First, find the volume of the cylinder:
Volume = π x r² x h
Volume = π x 5² cm x 10 cm
Volume = 250π cm³
Next, find the volume of the sphere:
Volume = 4/3 x π x r³
Volume = 4/3 x π x 5³ cm
Volume = 523.6 cm³
Finally, add the volumes of the cylinder and sphere together to get the total volume of the composite figure:
Total volume = 250π cm³ + 523.6 cm³
Total volume = 250π cm³ + 523.6 cm³
Total volume ≈ 1739.6 cm³
Therefore, the volume of the composite figure is approximately 1739.6 cm³.
Volume of Composite 3D Figures Practice
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