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 8th Grade

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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.

Part 1 of 4

Warm-up video

Lauren Kidman · 14:18

We don't generate video — this one is by Lauren Kidman on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.

Part 2 of 4

Key concepts

3 concepts

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.

Part 3 of 4

Practice

5 questions

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 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?

Part 4 of 4

Exit ticket

Quick comprehension check

“A bird feeder is made of a cylinder with a cone on top. The cylinder has a radius of 4 inches and a height of 6 inches. The cone has the same radius and a height of 3 inches. If a bird eats 2 cubic inches of birdseed per day, how many days will the bird feeder last when full?”

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Volume and Surface Area of Composite Figures

Objective

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