Pythagorean Theorem & Volume
Overview
Apply what you know about exponents and roots to geometry. You'll use the Pythagorean theorem to find missing sides of right triangles and compute the volume of cylinders, cones, and spheres.
Your progress
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About this unit
How to work through it
- Draw right triangles and label legs and hypotenuse before using a² + b² = c².
- Converse of Pythagorean theorem tests whether a triangle is right.
- Volume formulas: write each formula, then substitute with units cubed.
- Sketch 3-D figures and label radius, height, slant height as needed.
- Finish all exercises, geometry retention comes from repetition.
You should be able to
- Use the Pythagorean theorem to find missing sides.
- Apply the converse to classify triangles.
- Find volume of cylinders, cones, and spheres.
- Solve composite volume problems in context.
Key words
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Legs
- The two shorter sides of a right triangle that form the right angle.
- Cylinder
- A solid with two circular bases; volume V = πr²h.
- Sphere
- A perfectly round solid; volume V = (4/3)πr³.
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