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





Thanks for reading!


Here is a video explaining all of this.

Althea's Surface Area Growing Post,

Three-Dimensional shapes

Rectangular Prism
This is what it would look like when you make the rectangular prism into a net:
To calculate the surface area of a rectangular prism is you have to:

1st: find the area of a rectangle -multilpy the length by width -A= l x w 2nd: find the total surface area -add all the areas
__________________________________________________________________


A=l x w A=20 x 7 A=140 cm
TSA (Total Surface Area)= 140 + 24 + 24 = 188 cm ²
__________________________________________________________________ Triangular Prism
What it would look like when you make triangular prism into a net:
To calculate the surface area of a triangular prism is:

1st: find the area of a triangle -multiply base by height -divide by 2 -A= b x h /2 2nd: find the area of the rectangles -multiply length by width -A= l x w 3rd: find the total surface area -add all the areas ___________________________________________________________________

A= l x w A= 17 x 2 A= 34 mm²
TSA= 10 + 10 + 34 = 54 mm² ___________________________________________________________________ Cylinder
This is what it would look like if you make cylinder into a net:
To calculate the surface area of a cylinder is:

1st: find the circumference -If you have the diameter, what you have to do is multiply diameter by π (3.14) -πd=circumference -If you have the radius, what you have to do is multiply 2 by the radius because 2 radius makes diameter. -2r=diameter -So you have the diameter, what you have to do next is find the circumference by multiplying diameter by 3.14 * You need to find the circumference because you'll need it to get the are of a rectangle * 2nd: to find the area of a circle -You need to find the radius of a circle -area=π x r x r 3rd: Find the area of the rectangle ___________________________________________________________________

area of the circle is 50.24 cm²
TSA= 266.64 + 50.24 + 50. 24 = 366.72 cm²