1. WARM-UP Find the volume of each solid. 8 6 12 18 19 10 1213

2. SURFACE AREA PRISMS AND CYLINDERS

3. DEFINITIONS Prism: 3-D shape with two congruent bases. Surface Area: the sum of the areas of all the surfaces that bound the solid

4. PRISMS To understand surface area it helps to look at the “net” of the shape. 6m 8m 10m 10m 8m8m6m6m 6m 10m

5. PRISMS To find SA, you can just calculate the area of all the individual rectangles and add. 10m 8m 6m 10m 10(8)(2)=160 10(6)(2)=120 8(6)(2) = 96 SA = 376 m 2

6. PRISMS There is an alternative… 6 5 3 4 66 534 5 4 Notice the middle is one big rectangle The height is the same as the prism, and the length is the same as the perimeter of the base triangle. SA = area of two bases + area of big rectangle… SA = 2B + Ph SA = 2(0.5)(3)(4)+12(6) SA = 12 + 72 SA = 84 sq. units

7. PRISM - EXAMPLE 1. Find the surface area of the rectangular prism. Method 1: 7(5)(2) = 70 9(7)(2) = 126 9(5)(2) = 90 SA = 286 sq. units 9 5 7 Method 2: SA = 2B + Ph SA = 2(5)(7)+24(9) SA = 70 + 216 SA = 286 sq. units

8. PRISM - EXAMPLE 2. Find the surface area of the triangular prism. Method 1: 0.5(12)(5)(2) = 60 5(20) = 100 12(20) = 240 13(20) = 260 SA = 660 sq. units Method 2: SA = 2B + Ph SA = 2(0.5)(5)(12) + 30(20) SA = 60 + 600 SA = 660 sq. units 20 13 5 12

9. CYLINDERS There is one major difference between prisms and cylinders. With prisms, SA can be found using two different methods: break it up or use the formula: 2B+Ph With cylinders there is not a choice, the formula must be used.

10. CYLINDERS Let’s look at the “net” of a cylinder. 8 14 14 8 16  d =  (16)

11. CYLINDERS Use the formula for a prism: 2B+Ph. There is no perimeter, but there is circumference. The specific formula for SA of cylinder is… 14 8 16 d = (16) SA = 2  r 2 +  dh

12. EXAMPLE-CYLINDER 1. Find the surface area of the cylinder 8 14 SA = 2  r 2 +  dh SA = 2  8 2 +  (16)(14) SA = 128  + 224  SA = 352  sq. units (EXACT ANSWER) or SA = 1105.28 sq.units

13. EXAMPLE-CYLINDER 2. Find the surface area of the cylinder 18 27 SA = 2  r 2 +  dh SA = 2  9 2 +  (18)(27) SA = 162  + 486  SA = 648  sq. units (EXACT ANSWER) or SA = 2034.72 sq.units