Friday, February 26, 2010

Surface Area Growing Post

3-D Rectangles

This is a rectangular prism:

This is a rectangular prism net:

Here are the measurements needed to get the total surface area (TSA) of the rectangular prism:

Here are the measurements on the rectangular net:

You use the formula L x W = a (Length times Width equals area of rectangle).

A = L x W
A = 2 x 3
A = 6cm

Since all the squares have the same measurements, we can add up the TSA now.

TSA = S1 + S2 + S3 + S4 + S5 + S6
TSA = 6 + 6 + 6 + 6 +6 +6
TSA = 36cm²

3-D Triangles

This is a Triangular Prism:

A Triangular Prism Net:

Triangle Prism with the measurements needed to get total surface area:

Net with measurements:

To get the total surface area, you need the formulas:
A = B x H / 2 (Area equals Base times Height divided by two)
A = L x W

To get the TSA, I'll first add 5cm, 6cm, 7cm because they're technically one line and that I can just multiply that number by the 3 cm instead of having to do it multiple times.

5 + 6 + 7=18cm

a = L x W
a = 3 x 18
a = 54cm²

a = B x H / 2
a = 6 x 5
a = 30 / 2
a = 15cm²

Since the other triangle has the same dimensions, we'll just add up the TSA.

TSA = S1 + S2 + S3
TSA = 15 + 15 + 54
TSA = 84 cm²

So the Total Surface Area of this triangle is 84cm².


This is a Cylinder:

This is a Cylinder Net:

This is the Cylinder with the measurements:

This is the Cylinder net with measurements:

These are the formulas needed to get the total surface area of a cylinder:
C = pi.d (Circumference equals pi times diameter)
R = D / 2 (radius equals diameter divided by two)
A = pi.r.r (area of circle equals pi times radius times radius)
A = LxW (area equals length times width)

How to get the total surface area:

We don't have all the needed measurements like circumference and radius yet, so we'll get them.

C = pi x d C = 3.14 x 10 C = 31.4cm

Remember, the circumference of a circle becomes the length of a rectangle.

r = D / 2 r = 10 / 2 r = 5cm

Now we can get the areas of the circle and rectangle.

A = pi.r.r A = 3.14 x 5 x 5 A = 78.5cm²

A = L x W A = 31.4 x 10 A = 314cm²

Now to add them all up:

TSA = C1 + C2 + S1 TSA = 78.5 + 78.5 + 314 TSA = 471cm²

And here's a video that me and Jim and Feppe made that shows what I did in this scribepost in video form. :D

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