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## Surface Area and Volume

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**Surface Area and Volume**Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.**Definitions**• Surface area is the sum of the areas of all faces on a three dimensional object. • Surface area is measured in squared units. • Volume is the amount of space inside a three dimensional object. • Volume is measured in cubic units.**General Formulas**Total Surface Area TSA = 2B + (perimeter of base)(height of prism) Volume V = B(height of prism) B = the area of the base of the prism**Surface Area**Surface area is similar to the amount of wrapping paper needed to wrap a gift. To find surface area, you must find the 2-D areas of all the faces of the space shape. Add all of the areas together to find the total surface area. How many faces does a rectangular prism have? Top Back Left Right Front You should have said six. Bottom**Surface Area**Find the surface area of the rectangular prism. 4 in 6 in We’re going to have to find the area of all six faces. 15 in 4 in 4 in 6 in 6 in 6 in 4 in 15 in 15 in 15 in 15 in 6 in 4 in**Surface Area**Find the surface area of the rectangular prism. 4 in 6 in Find the area of all the rectangles. Remember that area for a rectangle is A = lw. 15 in 4 in 4 in 6 in 6 in 6 in 4 in A=24 in2 15 in 15 in 15 in 15 in 6 in 4 in A=60 in2 A=90 in2 A=90 in2 A=24 in2 A=60 in2**Surface Area**Find the surface area of the rectangular prism. 4 in Now add up all six areas. 6 in A = 60 + 60 + 90 + 90 + 24 + 24 = A = 60 + 60 + 90 + 90 + 24 + 24 = 348 in2 15 in 4 in 4 in 6 in 6 in 6 in 4 in A=24 in2 15 in 15 in 15 in 15 in 6 in 4 in A=60 in2 A=90 in2 A=90 in2 A=24 in2 A=60 in2**Surface Area**Find the surface area of the rectangular prism. 4 in 6 in You could also use the formula… 15 in**Surface Area**For a triangular prism, we can substitute into the general formula to come up with a formula that will work for all triangular prisms. TSA = 2B + (perimeter of base)(height of prism) Since the base is a triangle, you can replace B with ½bh. The new formula would be: TSA = 2(½bh) + (a+b+c)(height of prism) *a, b, and c are the sides of the triangle**Surface Area**TSA = 2(½bh) + (a+b+c)(height of prism) Let’s take a look at an example. Get rid of any sides you don’t need. First, label the triangle. a a, b, and c are the sides of the base (triangle). 15 in 15 in c 12 in h 22 in Height of prism 18 in b h is the height of the base (triangle).**Surface Area**TSA = 2(½bh) + (a+b+c)(height of prism) Now, plug the values into the formula to solve for the surface area. a 15 in 15 in c 12 in h 22 in Height of prism 18 in b**Volume**Volume is similar to how much water is inside a plastic water bottle. You are finding out how many cubic units are in a 3-D space shape. To the right, are examples of rectangular prisms broken up into cubic units.**Volume**Find the volume of the rectangular prism. 4 in 6 in The first step in finding volume is to find the area of the base (B). 15 in 6 in 15 in**Volume**Find the volume of the rectangular prism. 4 in 6 in Next we must take the area of the base and multiply it by the height of the prism. 15 in The formula for finding the volume of any prism is… where B is the area of the base and h is the height of the prism. Remember that Volume is measured in cubic units.**General Formula for Volume**You can use the following formula to find the volume of any prism. You can customize it to come up with formulas that work for specific shapes. V = (area of the base)(height of prism) Rectangular Prism: Triangular Prism: * *h = height of the triangle; H = height of the prism**Volume of a Triangular Prism**Let’s look at our triangular prism from a previous problem. What values would you need to plug in to find the volume? 15 in 18 is the base, 12 is the height of the triangle, and 22 is the height of the prism. 15 in 12 in 22 in 18 in**Volume of a Triangular Prism**15 in 15 in 12 in 22 in 18 in**Volume/Surface Area of a Cylinder**r The formula for the surface area of a cylinder is… h The formula for the volume of a cylinder is… If you have a problem where the diameter is given, remember to divide the diameter by two to get the radius.**Follow-Up Questions**Answer the following questions on loose leaf and hand them in to your teacher. Use 3.14 for pi.**Follow-Up Questions**Find surface area and volume of the following space shapes. Don’t forget units.**Follow-Up Questions**Find surface area and volume of the following space shapes. Don’t forget units. cm cm