What is a composite solid, and how do you determine whether to add or subtract the volumes of the individual shapes when finding the total volume?

A composite solid is a 3D shape made of two or more 3D solids. You add the volumes if the shapes are combined without overlap/removal, and subtract if one shape is cut out from another.

A rectangular prism has dimensions of 8 cm x 5 cm x 3 cm. A cylinder with a radius of 2 cm and a height of 5 cm is placed on top of the prism. What is the total volume of the composite shape?

The volume of the prism is 120 cm³. The volume of the cylinder is approximately 62.83 cm³. The total volume is approximately 182.83 cm³.

A birdhouse is made of a rectangular prism with a square pyramid on top. The prism is 10 inches wide, 10 inches long, and 6 inches tall. The pyramid has a base that is 10 inches by 10 inches and a height of 6 inches. What is the volume of the birdhouse?

The volume of the prism is 600 in³. The volume of the pyramid is 200 in³. The total volume is 800 in³.

A dessert is made by hollowing out a cone shape from a hemisphere (half sphere) of ice cream. The hemisphere has a radius of 5 cm. The cone that is removed has a radius of 3 cm and a height of 4 cm. What is the volume of the remaining ice cream?

The volume of the hemisphere is approximately 261.8 cm³. The volume of the cone is approximately 37.7 cm³. The volume of the remaining ice cream is approximately 224.1 cm³.

A silo consists of a cylinder with a hemisphere on top. The cylinder has a radius of 8 feet and a height of 20 feet. What is the surface area of the silo, not including the base?

The surface area of the cylinder (without the top) is approximately 1005.31 ft². The surface area of the hemisphere is approximately 804.25 ft². The total surface area is approximately 1809.56 ft².

Volume And Surface Area Of Composite Figures Lesson Plan for Grade 8th Grade

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Learning Objective

I can solve word problems involving volume and surface area of composite 3d figures made of cylinders, cones, spheres, rectangular prisms, and rectangular pyramids.

1
A composite shape is made up of more than one type of shape.
2
To calculate the surface area of a composite shape, you need to pick the parts of each shape's formula that you need.
3
To find the total surface area of a 3D composite shape, calculate the surface area of each individual part and then add them together.

Volume and Surface Area of Composite Figures

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Learning Objective

Warm-Up Video

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Practice Questions

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