SME
Grade 10 Math
Modeling with geometry: density, design and optimization
The main lesson, then each kind of problem it solves.
Modeling with geometry: density, design and optimization
Main lesson
Mass of a ball from its density
Use this for “A steel ball has radius 1.5 cm and steel is 7.8 g/cm³. Find its mass.”
Mass of a cone from its density
Use this for “A solid aluminum cone (2.7 g/cm³) has radius 3 cm and height 4 cm. Find its mass.”
Population density
Use this for “45,000 people live within 3 km of a town’s center. How many people per km²?”
Designing a can with the least material
Use this for “A can must hold 500 cm³. Which radius uses the least metal?”
The most area for a fixed perimeter
Use this for “40 m of fence makes a rectangular pen. Which sides give the most area?”