Monday, April 14, 2008

Robby's BOB

For the past 2 weeks, we learned how to find surface area's and volumes of 3-dimensional (3D) objects like rectangular prisms and cubes. Here is how to find the Surface area and Volume of a Rectangular Prism:

Surface Area of a Rectangular Prism

This is a Rectangular Prism. You can see the length, width, and height from any angle, meaning it is a meaning it is a 3D object.

Surface area is "how much wrapping you need to cover the whole object". So, if you were to cover it, you much wrapping would you need in a unit of measurement (not squared).

Our new Rectangular Prism has some measurements attached to it, so we can solve the surface area and Volume.

So:
Length = 6 cm
Width = 10 cm
Height = 6 cm

There is 1 formula for finding surface area:

-It is
(Area of L side + Area of R Side) +
(Area of Top) + Area of Bottom) +
(Area of Front + Area of Back)

O
ne important thing must be done to simplify finding the surface area. You must turn the rectangular prism into its 'Net' form, which is as follows:

Now do the equation (Since L side and R side, and Top and bottom, and Front and back have the same area, simply x2 to use less space.:

Surface Area
=
(Area of L side x 2) +
(Area of Top x 2) +
(Area of Front x 2)

=(60cm² x 2) + (36cm
² x 2)
+ (60cm
² x 2)
=(120cm
²) + (72cm²) + (120cm²)

=312cm
² is the Surface Area

Now Volume is pretty easy, there are 2 different ways on finding it.
One is : Length x Width x Height
the other one is Area of Base x Height

I'll do both to prove they both work:

The measurements are:
L = 6 cm
W = 10 cm
H = 6 cm

The Formula:
= Length x Width x Height
= 6cm x 10 cm x 6 cm
= 60 cm x 6
= 360 cm³ (note, the answer is CUBED or the power of 3 (³) because you are multiplying 3 dimensions together: length, width, and height)

The Second Formula is Area of Base x Height:
Area of Base = L
x W or L x H or W x H
Area of Base = L x W (for now)
Area of Base = 6cm x 10cm
Area of Base = 60cm²

Height = 6cm

60cm² x 6 = 360 cm³

See, the answer is 360cm³ for both, meaning they both work.
The Length x Width x Height one is easier, in my opinion, because it takes less work to do.
And that's how you find the volume and surface area of a Rectangular Prism.