Tuesday, April 11

Assignment: 10.4 on p. 532: 1-11. Topic: Density and problem solving with volume.

Topic: Density and problem solving with volume. Students should be able to use equations to find the missing lengths using the volume. For example in a triangular pyramid with volume 180, height of the base triangle = 12, and altitude of the pyramid = 6, we could first notice that the volume of a pyramid is

V = dfrac{1}{3}B cdot h

And then that B is the area of the triangular base, so B = dfrac{1}{2}bh_2. So we are essentially solving

V = dfrac{1}{3} cdot dfrac{1}{2} cdot b cdot h_2 cdot h

And we know all the values of variables except for b so we can re-arrange by the commutative property of multiplication

V = dfrac{1}{3} cdot dfrac{1}{2} cdot h_2 cdot h cdot {color{red}b}

With the known information we have

180 = dfrac{1}{3} cdot dfrac{1}{2} cdot 12 cdot 6 cdot {color{red}b}

So

180 = dfrac{1}{6} cdot 12 cdot 6 cdot {color{red} b}

Then

180 = 12{color{red} b}

And finally

15 = {color{red} b}