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Volume of Composite Solids

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Examples, solutions, and videos to help Grade 8 students learn how to determine the volume of a figure composed of combinations of cylinders, cones, and spheres.

New York State Common Core Math Grade 8, Module 7, Lesson 21

Download Worksheets for Grade 8, Module 7, Lesson 21

Lesson 21 Student Outcomes

• Students know how to determine the volume of a figure composed of combinations of cylinders, cones, and spheres.

Lesson 21 Summary

Composite solids are figures that are comprised of more than one solid. Volumes of composites solids can be added as long as no parts of the solids overlap. That is, they touch only at their boundaries.

Lesson 21 Classwork

Exercises 1–4
1. a. Write an expression that can be used to find the volume of the chest shown below. Explain what each part of your expression represents.
b. What is the approximate volume of the chest shown below? Use for 3.14 for π. Round your final answer to the tenths place.

2. a. Write an expression that can be used to find the volume of the figure shown below. Explain what each part of your expression represents.
b. Assuming every part of the cone can be filled with ice cream, what is the exact and approximate volume of the cone and scoop? (Recall that exact answers are left in terms of and approximate answers use for 3.14 for π). Round your approximate answer to the hundredths place.

3. a. Write an expression that can be used to find the volume of the figure shown below. Explain what each part of your expression represents.
b. Every part of the trophy shown is made out of silver. How much silver is used to produce one trophy? Give an exact and approximate answer rounded to the hundredths place.

4. Use the diagram of scoops below to answer parts (a) and (b). a. Order the scoops from least to greatest in terms of their volumes. Each scoop is measured in inches.
b. How many of each scoop would be needed to add a half-cup of sugar to a cupcake mixture? (One-half cup is approximately 7 in3.) Round your answer to a whole number of scoops.



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