March 27th, 2012, Aim: How do we find surface areas and lateral areas of prisms and cylinders ???

CYLINDERS AND PRISMS !!!   

A Cylinder is a three-dimensional geometric figure that has two congruent and parallel bases. 

A Prism is a solid with bases that are 2 congruent polygons and the other sides of a prism are lateral faces. 

Surface Area  is the measure of how much exposed area a solid object has.

Lateral Area is the surface area without the bases

CYLINDERS
To find surface area for a cylinder you have to use this formula : 

SA = LA + 2B 

Where SA stands for surface area LA stands for lateral area and B stands for the area of the base.

To find Lateral area for a cylinder the formula is : 2πrh

  

Example:

 

Steps

1. Find the lateral area. If you know the diameter of the cylinder is 4 and the formula to lateral area is 2πrh, you have to find the radius. so you divide 4 by 2 and the solution is 2.
2.  Plug it in. You now have the information to plug it into the formula. 2πrh where r is the radius and h is the height, so 2πrh is now 2π2*8.
3. Do the math. 2π2*8, first multiply 2*8, which is 16. Now its 2π16, so now you multiply 16 by 2 to find the solution which is 32π. You've found the Lateral area, so now you plug it into the surface area formula.
4.  Surface area formula. The formula is LA+2B. You have the LA but know you have to find B, where B is the Area of the base. To find the area of the base you have this formula, πr^2. You have the radius so now plug it in and solve. (π2^2 = 4π).
5. Put it all together. To find the surface area, the formula area is, LA +2B , so plug it in ! (32π+2(4π) = 32π+8π = 40π. The surface area is 40π.

PRISMS

 To find surface area for a prism you have to use this formula : 

SA = LA + 2B 

Where SA stands for surface area LA stands for lateral area and B stands for the area of the base.

To find Lateral area for a prism the formula is : LA=ph (Perimeter of the base and the height of the figure)

Example :

Steps

1. Find the lateral area. To find the lateral area you use the formula, LA=ph, so you have to multiply the perimeter of the base by the height. To find the perimeter if the base you add all the sides which are 13+13+17+17, which equals 60. so then multiply 60 by the height which is 6, (60*6= 360). The lateral area is 360.
2.   Surface area formula. The formula is LA+2B. You have the LA but know you have to find B, where B is the Area of the base. To find the area of the base you have this formula, h*w, which is 13*17 and it equals ,221.
3. Put it all together. To find the surface area, the formula area is, LA +2B , so plug it in ! (360 + 2(221) = 360 + 442 = 802) the surface area is 802.

Now you give it a try !!!

1. Whats the surface area?

  

2. Whats the Lateral area?

 

* WRITE ANSWERS IN COMMENTS BELOW* 

*images from hotmath .com*