Mrs. Bothers East Cobb Middle School (Adapted from Mr. Tauke’s PPT)

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Presentation transcript:

Mrs. Bothers East Cobb Middle School (Adapted from Mr. Tauke’s PPT)

Application: How much cardboard does it take to make a cardboard box? The manufacturers have to know this in order to make the boxes.

When wrapping gifts, you are covering the outside of the box. This is another example of surface area of a rectangular prism.

Looking at the net, you see that TO FIND THE SURFACE AREA OF A RECTANGULAR PRISM, YOU NEED TO FIND THE AREA OF ALL 6 FACES. Let’s explore this idea…

Do you see the RED (front) face? What are the dimensions of this rectangle? 10 in. 4 in.

Do you see another face that is just like the RED (front) face? Where is it located? Keep an eye on the next screen!

Yes, it’s on the back. 10 in. 4 in. 10 in. 4 in. FRONTBACK

Now there are 2 rectangles 40 in 2 that each have an area of 40 sq. in.

Do you see the BLUE (side) face? What are the dimensions of this rectangle? 4 in. 7 in.

Do you see another face that is just like the BLUE face? Where is it located?

Yes, it’s on the left side. 4 in. 7 in. 4 in. SIDE 1SIDE 2

Now there are 2 rectangles that each have an area of 28 sq. in. 28 in 2

Do you see the GREEN (top) face? What are the dimensions of this rectangle? 10 in. 7 in.

Do you see another face that is just like the GREEN face? Where is it located?

Yes, it’s on the bottom. 10 in. 7 in. 10 in. 7 in. BOTTOMTOP

Now there are 2 rectangles that each have an area of 70 sq. in. 70 in 2

Now we just need to add all the areas of the sides together in 2 28 in 2 40 in 2 28 in 2 70 in 2

The total Surface Area for this rectangular prism is = 276 in 2

2(lw) + 2(wh) + 2(lh) 2(40) + 2(28) + 2(70) in 2

Use the formula: 2(lw) + 2(wh) + 2(lh) 2(34) + 2(412) + 2(312) 2(12) + 2(48) + 2(36) cm 2

What is special about a cube? It has 6 square faces! Using the example to the left, what is the area of 1 face? 5 5 = 25 ft 2 Since there are 6 equal faces, what is the surface area? 6 25 = 150 ft 2 So, for SA of a cube, find the area of one face and then multiply by 6. What do you think the formula is? Yea, good job!! SA Cube = 6s 2 (s = length of one side)

What is the area of this cube, if its height is 8 in.? in 2

SA Rect. Prism = 2(lw) + 2(wh) + 2(lh) SA Cube = 6s 2 1) What is the surface area of a pizza box that has a length of 10 in, a width of 12 in, and a height of 2 in? 2)How much wrapping paper is needed to cover a box that is 7 cm long, 8 cm wide, and 3 cm tall? 3)What is the surface area of a Rubik’s Cube that is 3 inches tall? 4)Which has more surface area, a cube that is 10 in wide, or a rectangular prism that is 12 in wide, 10 in long, and 8 in tall? 1) 328 in2 2) 202 cm2 3) 54 in2 4) cube = 600in2, rect. prism = 592in2

Now, begin your homework. Be sure to use the correct formulas and SHOW ALL YOUR WORK!