


Mathematics Skill or Topic Area: The Volume of Spheres and Cylinders 

Next Gen Science Standards: ESS1: Earth’s Place in the Universe 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: CC.7.G.6 Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. 

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Engagement: Comets  It's Done With Math



Explore math connections with SpaceMath@NASA 

Problem I  Comparing the Volume of Vesta and the Moon  Astronomers often need to know the volume of the objects they study. Planets and large asteroids are distinctly spherical in shape. Students use this fact to estimate the volume of the asteroid Vesta in comparison to our own moon. Topics include scale and the volume of a sphere. [Open PDF] Problem II  The Magnetospheric, MultiScale Satellite Constellation.  Students determine how the MMS constellation satellites are stacked inside the third stage of an Atlas V rocket by using the properties of cylindrical volumes. Topics include scale and the volume of a cylinder. [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 that involves estimating the volume of an astronomical object or spacecraft. Explain why you set the problem up this way, and how you might find its answer. Evaluate your understanding: Challenge Problem  In 2010, NASA's Deep Impact spacecraft flew by the nucleus of Comet Hartley2. The images showed that its shape was dumbelllike, and could be approximated as a cylinder with a diameter of 0.5 kilometers and a height of 0.25 kilometers, and two spheres with diameters of 0.8 kilometers. About what is the volume of Hartley2 in cubic kilometers? Explain how you arrived at this answer. Answer: Using the formula for a sphere with a radius of 0.4 kilometers, the volume of each sphere is V = 0.27 cubic kilometers. The volume of the cylinder is just V = 0.05 cubic kilometers, so the total volume is V = 2 (0.27)+0.05 = 0.59 cubic kilometers.


NASA / JPL 3D Solar System 

Extend your new knowledge  Students use the Eyes on the Solar System simulator to study the volumes of spacecraft including the Hubble Space Telescope, CALIPSO and Kepler. They design a new Hubble Space Telescope with a larger volume and determine its mirror diameter. [ Open PDF ] 
