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.
Length = 6 cm
Width = 10 cm
Height = 6 cm
There is 1 formula for finding surface area:
(Area of L side + Area of R Side) +
(Area of Top) + Area of Bottom) +
(Area of Front + Area of Back)
One 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.:
=(Area of L side x 2) +
(Area of Top x 2) +
(Area of Front x 2)
=(60cm² x 2) + (36cm² x 2)
+ (60cm² x 2)
=(120cm²) + (72cm²) + (120cm²)
=312cm² 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
= 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.