Square roots arrive this week and they never leave. Everything after this, the Pythagorean theorem, the quadratic formula, distance on a graph, runs through them. The solids are a breather with one honest idea underneath: every prism and every cylinder has the same volume rule, and the only thing that changes is how you measure the bottom.
What you have to be able to do
Find the volume of a prism or a cylinder
Name the subsets of the real numbers
Evaluate square roots and higher roots, and multiply two square roots
The procedures
Volume of a prism or cylinder
Find the area of the base. This is the only part that changes between shapes.
Multiply by the height.
Area of the base times height. That is the whole rule, for every prism and every cylinder.
Working with square roots
The square root of a number is what you multiply by itself to get that number.
Two square roots multiplied become one square root of the product: the root of a times the root of b is the root of ab.
After multiplying, look inside for a perfect square factor and pull it out.
Worked
WORKED
Find the volume of a cylinder with radius 3 and height 10. Base is a circle: area = πr2 = 9π. Times the height, 10. ANSWER: 90π cubic units
WORKED
Multiply the square root of 8 by the square root of 2. Combine under one radical: the root of 16. ANSWER: 4
Terms
Term
Meaning
prism
a solid with two identical parallel bases joined by flat sides
radicand
the number sitting under the radical sign
irrational number
a number that cannot be written as a fraction of two integers
Check yourself
1. Volume of a prism with base area 12 and height 5
2. The square root of 9 times the square root of 4
3. Is the square root of 2 rational or irrational?
reveal answers
60 · 6 · irrational
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 16, solids, subsets, and square rootsalgebra 1 · oda