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# 12 1 solids

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### 12 1 solids

1. 1. SOLIDS PRISMS AND CYLINDERS JIM SMITH JCHS CYLINDERS PRISMS spi3.2.K, 4.3.A
2. 2. REVIEW AREA AND PERIMETER <ul><li>PERIMETER OF ANY POLYGON = ADD ALL SIDES </li></ul><ul><li>AREA OF RECTANGLE = lw </li></ul><ul><li>We’ll call circumference - perimeter </li></ul><ul><li>PERIMETER OF CIRCLE = 2 π r </li></ul><ul><li>AREA OF CIRCLE = π r² </li></ul>
3. 3. FIND THE PERIMETER AND AREA 6 4 A = lw A = 6 ∙ 4 A = 24 P = add sides P = 4+6+4+6 P = 20
4. 4. FIND THE PERIMETER AND AREA Remember- call circumference perimeter P = 2 π r P = 2 π 5 P = 10 π A = π r² A = π 5² A = 25 π We’ll use B for base area 5
5. 5. Perimeter of base LATERAL AREA (SIDES or LABEL) LA = Ph l w h l w l w h
6. 6. Bottom B SURFACE AREA (INCLUDES TOP & BOTTOM) SOMETIMES CALLED TOTAL AREA SA = LA + 2B l w h Top B Lateral Area LA
7. 7. BASE AREA ( B ) TELLS THE NUMBER OF CUBES NEEDED TO FILL THE BASE THE HEIGHT ( h ) TELLS THE NUMBER OF LAYERS OF CUBES VOLUME ( How Much It Will Hold ) VOL = Bh
8. 8. <ul><li>LATERAL AREA (SIDES OR LABEL ) </li></ul><ul><li>LA = Ph </li></ul><ul><li>SURFACE AREA (INCLUDES TOP and </li></ul><ul><li>BOTTOM SOMETIMES CALLED TOTAL AREA ) </li></ul><ul><li>SA = LA + 2B </li></ul><ul><li>VOLUME (HOW MUCH IT WILL HOLD) </li></ul><ul><li>VOL = Bh </li></ul>FORMULAS
9. 9. PRISM ( find P and B first ) l = 4 w = 3 h = 7 P = 4+3+4+3 = 14 B = 4 x 3 = 12 LA = Ph = 14 x 7 = 98 sq units SA = LA + 2B = 98 + 24 = 122 sq units Vol = Bh = 12 x 7 = 84 cubic units 4 3 7
10. 10. r = 3 h = 6 P = 2 π r = 6 π B = π r² = 9 π LA = Ph = 6 π x 6 = 36 π sq units SA = LA + 2B = 36 π + 18 π = 54 π sq u N VOL = Bh = 9 π x 6 = 54 π cu units CYLINDER 6 3
11. 11. CONES PYRIMIDS AND
12. 12. PARTS OF A PYRIMID ( SQUARE BASE ) BASE EDGE BASE EDGE HEIGHT ( h ) SLANT HEIGHT ( l )
13. 13. PARTS OF CONES HEIGHT ( h ) r SLANT HEIGHT ( l )
14. 14. FORMULAS LA = ½ P l SA = LA + B VOL= ⅓ B h
15. 15. FIND THE PERIMETER AND AREA FIRST 12 Base edge h sl 12 8 10 P = 12 + 12 + 12 + 12 = 48 B = 12 x 12 = 144 LA = ½ P l = ½ x 48 x 10 = 240 sq un SA = LA + B = 240 + 144 = 384 sq un VOL = ⅓ B x h = ⅓ 144 x 8 = 384 cu un
16. 16. 3 r h sl 3 4 5 P = 2 π r = 2 π 3 = 6 π B = π r ² = π 3² = 9 π LA = ½ P l = ½ x 6 π x 5 = 15 π sq un SA = LA + B = 15 π + 9 π = 24 π sq un VOL = ⅓ B h = ⅓ x 9 π x 4 = 12 π cu un