## 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.