## Friday, March 9, 2012

### Norien's Surface Area and Volume Post

Rectangular Prism
Shape/ Net:

Solution:
To find the total surface area (TSA) of a rectangular prism, the first step is to find the areas of the six faces of a rectangular prism. To find the areas, you have to find the lxw of the top, front, and side to get the area of one face. 5x10= 50 m2 (Top), 6x10= 60m2 (Front), and 6x5= 30m2 . Once you have the lxw of the top, front, and side of the faces, you add it all up and get 140. With the 140 you multiply it by two to get all six faces of the rectangular prism and the answer to the total surface area would be 280 m 2

lxw
5x10 = 50 m 2
6x10 = 60 m 2
6 x 5 = 30 m 2

TSA = 2(T+F+S)
= 2(50+60+30)
= 2(140)
= 280 m 2

Triangular Prism
Shape/ Net:
Solution:
To find the total surface area (TSA) of a triangular prism, the first step is to find the areas of the three faces of the rectangles in a triangular prism. You have to multiply the length and width. To find the length you have two choices, you can either multiply it one by one like, 10x5, 9x5, and 8x5 or you can add the 10cm, 9cm, and 8cm and multiply it by the width which would both equal to 135cm 2 . After finding the area of the rectangle faces, you have to find the triangle faces. To find the rectangular faces, you have to use the formula, which is to multiply the base by the height and divide it by two. 8x9 = 72, 72/2 = 36 cm2 . After you find all those areas you add them all together (NOTE: Don't forget to add another 36 because there are 2 triangles in a triangular prism), the answer would be 207cm 2

lxw
= 27x5
= 135 cm 2
= 36 cm 2
= 36 cm 2
-----------
207cm 2
bxh
--------
2

8x9
--------
2
72
------
2
= 36 cm 2

Cylinder
Shape/ Net:
Solution:
To find the total surface area (TSA) of a cylinder, the first step is to find the radius if they give you the diameter, or find the diameter if they give you the radius because you will need both.
In this cylinder they gave us the diameter which means we will need to find the radius and to find that we need to divide the diameter in to two, which would mean we would have to divide 8 by 2 and get 4mm. The next step would be to find the circumference of the rectangle. To find that you will need to use the formula which is c= π d, c= 3.14x8, c= 25.12mm. Next you will multiply the length times the width of the rectangle. The length would be 25.12 and the width be 12 and when you multiply those two together the answer would be 301.44mm 2 . Next, you will find the area of the circle and to do that you use the formula; a= π r, a= 3.14x4, a= 3.14x16, a= 50.24mm 2 . Lastly, you have to add the area of the rectangle (301.44) and the two circles (50.24) together which would get you, 401.92mm 2

If you did not understand my explanation or need more examples, here is a link.

Volume

Volume of Rectangular Prism
To find the volume of a rectangular prism, you have to multiply the length, width, and height together. Remember: It doesn't matter which one you multiply first because technically they will all equal to the same number, no matter the order.
v= l x w x h
v= 16 x 20 x 8
v= 2560 cm 3

Triangular Prism
To find the volume of a triangular prism, you have to multiply the base and height and divide it by 2, to get the area of the triangle. Then you have to multiply the second height (non- triangle number) by the answer to the area of the triangle.
v= (b x h1 / 2) x h2
v= (3 x 5 / 2) x 8.5
v= (15 / 2) x 8.5
v= 7.5 x 8.5
v= 63.75 m 3

Cylinder
To find the volume of a cylinder, you have to use the formula, π r 2h. First, you have to find the radius by dividing the diameter by 2. Then you have to square the radius and then multiply the 3.14 by the answer you got
for the radius and then multiply it by the height of the cylinder.
r= d/2
r= 12/2
r= 6cm

v= π r 2h
v= 3.14 x 6 2 x 15
v= 3.14 x 36 x 15
v= 1695.6 cm 3

How To Get the Volume of a Fraction of a Triangular Prism
To get the volume of a triangular prism is already on my post (second one). But What isn't on mine is how to get a fraction of a triangular prism. First you have to divide the numerator by the denominator and the decimal you get from that, you have to multiply it by the answer you got from the triangular prism volume.
v= (bxh1/ 2) x h2
v= (4x8/ 2) x 6.5
v= (16/ 2) x 6.5
v= 8 x 6.5
v= 52cm 3

fraction : 3/ 8 = 0.375
0.375 x 52 = 19.5 cm 3