Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Moving Stonehenge

Age 16 to 18
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions

If transporting the stones dry, the minimum volume of wood required:

$(V_{stone}\rho_{stone} + V_{wood}\rho_{wood})g = V_{wood}\rho_{water}g$
$\therefore V_{wood}(\rho_{water} - \rho_{wood}) = V_{stone}\rho_{stone}$
$\therefore V_{wood} = \frac{V_{stone}\rho_{stone}}{\rho_{water} - \rho_{wood}} = 13.05m^3$
$V_{wood}/(\pi r_{tree}^2) = length_{tree} = 415.4m$

That's nearly half a kilometer of sizeable trees!

If the stones could be transported wet, which would of course require a river about 2 feet deeper, then less wood would have been required:

$(V_{stone}\rho_{stone} + V_{wood}\rho_{wood})g = (V_{wood} + V_{stone})\rho_{water}g$
$\therefore V_{wood}(\rho_{water} - \rho_{wood}) = V_{stone}\rho_{stone}$
$\therefore V_{wood} = \frac{V_{stone}(\rho_{stone} - \rho_{water})}{\rho_{water} - \rho_{wood}} = 8.55m^3$
$V_{wood}/(\pi r_{tree}^2) = length_{tree} = 272.2m$

That's still a lot of trees, but considerably fewer, maybe 25 large trees. That is the absolute minimum value though, at which the object will have neutral buoyancy, i.e. will have the overall density of water.


You may also like

Keep Your Momentum Going

A look at a fluid mechanics technique called the Steady Flow Momentum Equation.

Mach Attack

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo