Thursday, February 25, 2010

Laura's Surface Area Growing Post

In order to find the surface area of this cylinder, we have to first find the areas of all of the shapes it's made out of.

To find the area of a circle we need to find the radius first.

r= d/2

r= 3/2

r= 1.5

Area of a circle= pi X r X r

= 3.14 X 1.5 X 1.5

= 7.06 squared centimeters

Now we multiply by 2 because there are 2 circles.

7.06/2= 3.53 squared centimeters

To find the area of a rectangle we need to find the circumference of the circle first.

C= pi X d

C= 3.14 X 3

C= 9.42

Area of a rectangle= L x W

= 20 x 9.42

= 188.4 squared centimeters

Now we add the 2 numbers together.

188.4 squared centimeters + 3.53 squared centimeters = 191.93 squared centimeters

We already know the area of all of the shapes this triangular prism is made of from the net. Here is how they were calculated:

rectangles= L x W

= 2 x 15

= 30 squared centimeters

triangles= B x H/2

= 15 x 5/2

= 75/2

= 37.5

Now we have to add all of the areas together to get the total surface area.

(30 x 4) + (37.5 x 2)= TSA

120 + 75=TSA

195 squared centimeters= TSA

Again, we already have the areas of the shapes that make this rectangular prism. They are all rectangles so they were all calculated with the same formula: L x W.

Now to add them all together:

(50 x 4) + (10 x 2) = TSA

200 + 20 = TSA

220 = TSA

VOCABULARY:

TSA = total surface area

L = length

W = width

B = base

H = height

pi = 3.14

Here is a video explaining all of this.