Instructional Activity# Hemispheres in Boxes

Lesson 19. Unit 5. Grade 8 Open Up Resources

Open Up Resources15 min(s)

This Instructional Activity is a part of the Lesson 19, Unit 5, Grade 8. In this activity, students think about a hemisphere fitting inside the smallest possible box (or rectangular prism). Students reason that the smallest box in which a hemisphere can fit has a square base with edge length that is the same as the diameter of the hemisphere, and its height will be the radius of the hemisphere. Further, if we calculate the volume of the box, we have an upper bound for the volume of the hemisphere. This activity prepares students for the next, where they will calculate the upper and lower bounds for the volume of a hemisphere by considering cylinders and cones that fit outside or inside the hemisphere.