SOLIDSSOLIDSPRISMS AND PRISMS AND CYLINDERSCYLINDERS

JIM SMITH JCHSJIM SMITH JCHSspi3.2.K, 4.3.Aspi3.2.K, 4.3.A

REVIEW AREA AND PERIMETERREVIEW AREA AND PERIMETER

• PERIMETER OF ANY POLYGONPERIMETER OF ANY POLYGON = ADD ALL SIDES= ADD ALL SIDES

• AREA OF RECTANGLE = lwAREA OF RECTANGLE = lw We’ll call circumference - perimeterWe’ll call circumference - perimeter

• PERIMETER PERIMETER OF CIRCLE = 2OF CIRCLE = 2ππrr

• AREA OF CIRCLE = AREA OF CIRCLE = ππr²r²

FIND THE PERIMETER AND AREAFIND THE PERIMETER AND AREA

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A = lwA = lwA = 6A = 6∙∙44A = 24A = 24

P = add sidesP = add sidesP = 4+6+4+6P = 4+6+4+6P = 20 P = 20

FIND THE PERIMETER AND AREAFIND THE PERIMETER AND AREA

Remember- call circumference perimeterRemember- call circumference perimeter

55

P = 2P = 2ππrrP = 2P = 2ππ55P = 10P = 10ππ

AA = = ππr²r²A = A = ππ5²5²A = 25A = 25ππ

We’ll use We’ll use BB for base area for base area

llww

hh

l w l wl w l w

hh

Perimeter of basePerimeter of base

LATERAL AREALATERAL AREA (SIDES or LABEL)(SIDES or LABEL)

LA = PhLA = Ph

llww

hh

Top Top BB

Bottom Bottom BB

SURFACE AREASURFACE AREA (INCLUDES TOP & BOTTOM)(INCLUDES TOP & BOTTOM)

SOMETIMES CALLED TOTAL AREASOMETIMES CALLED TOTAL AREA

SA = LA + 2BSA = LA + 2B

Lateral Area Lateral Area LALA

BASE AREA ( BASE AREA ( B B ) TELLS) TELLSTHE NUMBER OF CUBESTHE NUMBER OF CUBESNEEDED TO FILLNEEDED TO FILLTHE BASETHE BASE

THE HEIGHT ( THE HEIGHT ( h h ) TELLS THE ) TELLS THE NUMBER OF LAYERS OF CUBESNUMBER OF LAYERS OF CUBES

VOLUMEVOLUME (How Much It Will Hold)

VOL = BhVOL = Bh

LATERAL AREALATERAL AREA (SIDES OR LABEL(SIDES OR LABEL))

LA = PhLA = Ph

SURFACE AREASURFACE AREA (INCLUDES TOP and(INCLUDES TOP and

BOTTOMBOTTOM SOMETIMES CALLED SOMETIMES CALLED TOTAL AREATOTAL AREA))

SA = LA + 2BSA = LA + 2B

VOLUMEVOLUME (HOW MUCH IT WILL HOLD)(HOW MUCH IT WILL HOLD)

VOL = BhVOL = Bh

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PRISM (PRISM (find P and B firstfind P and B first )) ll = 4 w = 3 h = 7 = 4 w = 3 h = 7

P = 4+3+4+3 = 14P = 4+3+4+3 = 14 B = 4 x 3 = 12B = 4 x 3 = 12

LA = Ph = 14 x 7 = 98LA = Ph = 14 x 7 = 98 sq unitssq units

SA = LA + 2B = 98 + 24 = 122SA = LA + 2B = 98 + 24 = 122 sq unitssq units

Vol = Bh = 12 x 7 = 84Vol = Bh = 12 x 7 = 84 cubic unitscubic units

r = 3r = 3 h = 6h = 6 P = 2P = 2ππr = 6r = 6ππ B = B = ππr² = 9r² = 9ππLA = Ph = 6LA = Ph = 6ππ x 6 = 36 x 6 = 36ππ sq unitssq units

SA = LA + 2B = 36SA = LA + 2B = 36ππ + 18 + 18ππ = 54 = 54ππ sq usq uNN

VOL = Bh = 9VOL = Bh = 9ππ x 6 = 54 x 6 = 54ππ cu unitscu units

CYLINDERCYLINDER

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CONESCONES

PYRIMIDSPYRIMIDS

ANDAND

PARTS OF A PYRIMIDPARTS OF A PYRIMID( SQUARE BASE )( SQUARE BASE )

BASE EDGEBASE EDGE

BASE EDGEBASE EDGE

HEIGHTHEIGHT ( h ) ( h )

SLANT HEIGHT ( SLANT HEIGHT ( ll ) )

PARTS OF CONESPARTS OF CONES

HEIGHT ( h )HEIGHT ( h )

rr

SLANT HEIGHT ( SLANT HEIGHT ( ll ) )

LA = LA = ½½ P P ll

SA = LA + BSA = LA + B

VOL= VOL= ⅓⅓ B h B h

FIND THE PERIMETERFIND THE PERIMETER AND AREA FIRSTAND AREA FIRST

1212

Base edge Base edge hh sl sl 12 12 88 1010

P = 12 + 12 + 12 + 12 = 48P = 12 + 12 + 12 + 12 = 48B = 12 x 12 = 144B = 12 x 12 = 144

LA = ½ P l = ½ x 48 x 10 = LA = ½ P l = ½ x 48 x 10 = 240 sq un240 sq unSA = LA + B = 240 + 144 = SA = LA + B = 240 + 144 = 384 sq un384 sq unVOL = ⅓VOL = ⅓ B x h = B x h = ⅓⅓ 144 x 8 = 144 x 8 = 384 cu un384 cu un

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r r hh slsl3 3 44 55

P = 2 P = 2 ππ r = r = 2 2 ππ 3 = 6 3 = 6 ππB = B = ππ r r² = ² = ππ 3² = 9 3² = 9 ππ

LA = ½ P l = ½ x 6 LA = ½ P l = ½ x 6 ππ x 5 = 15 x 5 = 15 ππ sq unsq un

SA = LA + B = 15 SA = LA + B = 15 ππ + 9 + 9 ππ = 24 = 24 ππ sq unsq un

VOL = ⅓ B h = ⅓ x 9 VOL = ⅓ B h = ⅓ x 9 ππ x 4 = 12 x 4 = 12 ππ cu uncu un