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Understanding Surface Area and Volume of Prisms and Cylinders in Real-World Contexts

In this lesson, students will explore the importance of calculating the surface area and volume of three-dimensional solids, specifically prisms and cylinders. Through engaging activities, including a real-world bonus question, learners will understand how these calculations apply to everyday situations, like cleaning windows. The lesson will define key terms such as polyhedron, lateral faces, and altitude. Students will also work in groups to complete exercises on finding surface areas, preparing to present their findings. Homework will reinforce the concepts learned.

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Understanding Surface Area and Volume of Prisms and Cylinders in Real-World Contexts

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  1. Warm UP • Grab a Unit 10 Packet from front • Complete page 2 10 minutes End

  2. Surface Area and Volume Unit 10

  3. Essential Questions • Why is it important to calculate surface area & volume of 3D solids? • What sorts of real-world situations require knowledge of surface area and volume?

  4. Bonus Question • You are cleaning all the windows in your house with window cleaner and a roll of paper towel. When you start, the paper towel roll is 8 inches wide. After you clean the windows, your paper towel roll is only 3 inches wide. How much surface area did you lose? (A paper towel roll is 1 foot tall)

  5. Today’s Objective • Students will be able to find the surface area of prisms and cylinders

  6. Definitions Polyhedron – a 3-D figure whose surfaces are polygons (flat) Each polygon is called a FACE. An EGDE is where 2 faces meet. A VERTEX is where 3 or more edges meet. EDGE VERTEX FACE FACE FACE

  7. Prisms • Definition: A Prism is a polyhedron with exactly two congruent, parallel faces, called bases. • Lateral Faces – faces that are not the bases. • Altitude – height of prism ( to both bases) • Lateral Area – sum of the areas of the lateral faces • Surface Area – sum of lateral area AND areas of bases

  8. Examples of Prisms

  9. Prism Formulas

  10. Ex 1: Find the lateral and Surface Areas LA = SA =

  11. Ex 2: Find the Lateral and Surface Area LA = SA =

  12. Ex 3: Find the Lateral and Surface Areas LA = SA =

  13. Cylinder: • Definition: A Cylinder is a prism with circular bases • Formulas:

  14. Example 4: FindLateral and Surface Areas LA = SA =

  15. Ex 5: Find the Lateral and Surface Areas LA = SA =

  16. Classwork • Arrange desks in groups • As a group, complete the right side of page 2 of Unit 10 packet • Be prepared to have your work displayed on doc cam!

  17. Homework • Complete page 2 of Unit 10 packet

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