## Tuesday, February 1, 2011

### Cylinder Math Notes

When we think of cylinders we need to better understand circles.

Circle Terms
Diameter- Cuts the circle in half
Circumference- The perimeter of the circle
Pi- The ratio between circumference:diameter or 3.14
Formulas
Circumference- pi x diameter = circumference
Diameter- 2 x radius = d or circumference/ pi = diameter
Area of a Circle
To find the area of a circle you use the equation:
pi x r2
It means multiply pi by the radius squared
Homework
Our homework is to find the area, diameter, circumference and radius of these circles. I'll do the circles in order from left to right
a) d = c/pi r = d/2 a = pi x r2
d = 18.89/3.14 r = 6/2 a = 3.14 x 3 x 3
d = 6cm r = 3cm a = 28.26cm2

b) d = c/pi r = d/2 a = pi x r2
d = 31.4/3.14 r = 10/2 a = 3.14 x 5 x 5
d = 10cm r = 5cm a = 78.5 cm2

c) d = r x 2 c = pi x d a = pi x r2
d = 3.2 x 2 c = 3.14 x 6.4 a = 3.14 x 3.2 x3.2
d = 6.4cm c = 20.1cm a = 32.15cm2

d) d = r x 2 c = pi x d a = pi x r2
d = 6 x 2 c = 3.14 x 12 a = 3.14 x 6 x6
d = 12cm c = 37.68cm a = 113.04cm2

e) d = r x 2 c = pi x d a = pi x r2
d = 16.5 x 2 c = 3.14 x 33 a = 3.14 x 16.5 x 16.5
d = 33cm c = 103.62cm a = 854.87cm2

f) r = d/2 c = pi x d a = pi x r2
r = 25/2 c = 3.14 x 25 a = 3.14 x 12.5 x 12.5
r = 12.5cm c = 78.5cm a = 490.63cm2

g) r = d/2 c = pi x d a = pi x r2
r = 15/2 c = 3.14 x 15 a = 3.14 x 7.5 x 7.5
r = 7.5cm c = 47.1cm a = 176.63cm2

I had problems organizing the equations for the homework. If anyone has a suggestion to organize the homework please do comment. :)
I hope everyone now knows how to find the different parts of a circle.

Cylinder Volume and Volume Problems
Here is a problem from 7.3 to better understand calculating the volume of a cylinder. To solve this cylinder problem we will need the formula: π x r x r x h
But we dont have the radius. We have the diameter. We will need the formula to find the radius: d/2 = r. In this question d= 20.3cm
20.3/2 = 10.15cm
Now we can do the formula
π x r x r x h = v
3.14 x 10.15 x 10.15 x 10 = 3234.9065cm^3

Here is a question from 7.4. For this one we have to subtract the small cylinder from the big cylinder.
Big circle
pi x r x r x h = v
3.14 x 0.5 x 0.5 x 10 = v
7.85m^3 = v

Small circle
pi x r x r x h = v
3.14 x 0.4 x 0.4 x 10 = v
5.024m^3 = v

7.85 - 5.024 = 2.826m^3
Rounded it is 2.8m^3.

1. Awesome job Nils, I love how you had ALL of that color it really brought out the answers and different subject for each. Another thing that you could have done better, could've been to upload a photo. And don't worry you laid it out fine. Over all VERY good job . :)

2. Great job Nils.Your post is very neat and understandable.I really like the colors you used, it really made the post standout.Once again great job and keep it up!

3. Good job Nils! Your post was easy to understand and well organized with the color.

4. Good job Nils! You included all the information that we talked about that class. Even though you had trouble organizing the equations, you still made it clear and easy to understand because of the colours you made them! Next time, try to separate the sections (like the circle terms and formulas etc. at the top) more so they are not all squished together. Other than that, great job!

5. Great job Nils! I liked how you had all the notes we went over in class today included in your post. The way you organized your answers at the bottom was just fine because of the colours you used. It was also a good thing that you included a reminder of the homework for us. But maybe next time you could have pictures for things such as radius and diameter to give us a better understanding of the term. Another suggestion I have is that you show us the actual formula instead of having it in words, but you probably don't know how and neither do I, so the way you did it was just fine. Keep up the great work Nils!