


Mathematics Skill or Topic Area: Volumes of Spheres, Cylinders and Cones 

Next Gen Science Framework ESS2.C The role of water in Earth’s surface processes; ESS3.B Natural resources; LS2.B Cycles of matter and energy transfer in ecosystems; PS1.A Structure of matter; PS2.C Stability and instability in physical systems; ETS1.A: Defining and Delimiting an Engineering Problem; ETS1.B: Developing Possible Solutions; ETS1.C: Optimizing the Design Solution Common Core ELA for Science: RST.68.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.RST.68.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.68.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic. Common Core Math Standard: CCSS.8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.


Video Engagement: Environmental Control on the ISS Learn how engineers turn perspiration into innovation on the International Space Station so astronauts can live and work comfortably. The Environmental Control and Life Support System, or ECLSS, regulates the environment, including temperature, humidity and breathable air. (5 minutes). View Program 


Explore math connections with SpaceMath@NASA 

Problem I  The Interior Volume of the Crew Habitation Module  Students use the volume formula for a cylinder, and actual dimensions of the Crew Habitation Module (CHM) to determine the volume available to crew members inside the CHM, allowing for the thickness of the walls. [ Open PDF ] Problem II  Spherical Storage Tanks  Imagine replacing the cylindrical CHMs with a series of spherical habitats linked together. In this problem, students determine how many spherical habitats must fit together to equal the volume of a cylindrical module with the same diameter. [ Open PDF ] Explain your thinking: Write your own problem  Using information found in the Math Connection problems, the press release or the video program, create your own math problem. Explain why you set the problem up this way, and how you might find its answer. Evaluate your understanding: Challenge Problem 1  The Conical Storage Tanks A conical tank is often used by astronauts to store and transfer liquids. In this problem, students explore the volume of a conical storage tank and determine where to put a mark to let astronauts know when the tank is halffull. [ Open PDF ] Challenge Problem 2  The conical Inflatable Heat Shield Hypersonic Inflatable Aerodynamic Decelerators (HIAD) are new technology NASA is exploring to create heat shields that are inflatable, take up less space, and capable of landing humans and large payloads safely on Earth and Mars. Inflated just before entering the atmosphere, they are conical in shape, and able to withstand the high temperatures of reentry.In this problem, students explore the volume and surface areas of various HIAD heat shields. [ Open PDF ] [ Open eClips Video ]


NASA / JPL 3D Solar System 

Extend your new knowledge  Science fiction stories often show a space station shaped like a donut  a shape called a torus. Students estimate the total volume of the ISS, and determine the diameter of a donutshaped space station that has the same volume. [ Open PDF ] 
