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Core Conundrum: A 'Pi in the Sky' Math Challenge

Lesson .

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Core Conundrum: A 'Pi in the Sky' Math Challenge

Jet Propulsion Laboratory https://www.jpl.nasa.gov/ Last Updated: June 20, 2025
Subject
Math
Grade Levels
9-12
Time Required
30 - 60 mins
Standards .
Math Standards (CCSS - Math)
.

Reason quantitatively and use units to solve problems.

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Overview

The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the ninth set, students use the mathematical constant pi to calculate the volume and density of Mars' liquid core.

Materials

  • Pi in the Sky 9: Core Conundrum worksheet – download PDF
  • Pi in the Sky 9: Core Conundrum answer key – download PDF (also available as a text-only doc)

Background

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Core Conundrum

Since 2018, the InSight lander has studied the interior of Mars by measuring vibrations from marsquakes and the “wobble” of the planet as it rotates on its axis. Through careful analysis of the data returned from InSight, scientists were able to measure the size of Mars’ liquid core for the first time and estimate its density. In Core Conundrum, students use pi to do some of the same calculations, determining the volume and density of the Red Planet’s core and comparing it to that of Earth’s core.

educators.

Teachable Moments: Pi Goes to Infinity and Beyond in NASA Challenge

Learn more about about pi, the history of Pi Day before, and the science behind the 2022 NASA Pi Day Challenge.

Procedures

Core Conundrum

The InSight Mars lander is equipped with several tools to help scientists learn more about the interior of the Red Planet, including a seismometer that detects marsquakes. By measuring the vibrations that travel across the surface of Mars and through its interior layers, scientists were able to accurately measure the size of Mars’ liquid core and estimate its density. Knowing the size and density of Mars' core will help us learn more about how the planet formed, how its magnetic field developed, and what materials make up the core, which will ultimately lead to a better understanding of how Earth and other planets form.

If Mars' core has a mass of 1.54 x 1023 kg and a radius of 1,830 km, as measured by InSight, what is the density of the core?

How does that compare to the density of Earth’s core, which ranges from 10 to 13 g/cm3?

What does that tell us about the makeup of Mars’ core?

› Learn more about the InSight lander

The InSight lander is shown on the surface of Mars, where circular lines radiate out from a central point. The interior of Mars is shown with lines flowing left and right from the same central point and extending from the crust into Mars’ mantle down t...

Assessment

Illustrated answer key for the Core Conundrum problem

› Download text-only answer key (doc)

Extensions

Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

educators.

Pi Day Challenge Lessons

Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

students.

Slideshow: NASA Pi Day Challenge

The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

Blogs and Features

students.

How Many Decimals of Pi Do We Really Need?

While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

students.

Slideshow: 18 Ways NASA Uses Pi

Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

Related Lessons for Educators

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Planetary Egg Wobble and Newton's First Law

Students try to determine the interior makeup of an egg (hard-boiled or raw) based on their understanding of center of mass and Newton’s first law of motion.

Related Activities for Students

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Mars in a Minute: Are There Quakes on Mars?

Are there earthquakes on Mars – or rather, "marsquakes"? What could they teach us about the Red Planet?

Multimedia

students.

Downloads

Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

students.

Infographic: Planet Pi

This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

Recursos en español

students.

18 Maneras en Que la NASA Usa Pi

Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.

  • Mars Quick Facts

Facts and Figures

  • Mars

Missions and Instruments

  • Mars InSight Lander

Websites

  • Mars Exploration
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