SOLIDS PRISMS AND CYLINDERS JIM SMITH JCHS spi3.2.K, 4.3.A

REVIEW AREA AND PERIMETER PERIMETER OF ANY POLYGON = ADD ALL SIDESPERIMETER OF ANY POLYGON = ADD ALL SIDES AREA OF RECTANGLE = lwAREA OF RECTANGLE = lw We’ll call circumference - perimeter We’ll call circumference - perimeter PERIMETER OF CIRCLE = 2πrPERIMETER OF CIRCLE = 2πr AREA OF CIRCLE = πr²AREA OF CIRCLE = πr²

FIND THE PERIMETER AND AREA 6 4 A = lw A = 6∙4 A = 24 P = add sides P = P = 20

FIND THE PERIMETER AND AREA Remember- call circumference perimeter 5 P = 2πr P = 2π5 P = 10π A = πr² A = π5² A = 25π We’ll use B for base area

l w h l w l w h Perimeter of base LATERAL AREA (SIDES or LABEL) (SIDES or LABEL) LA = Ph

l w h Top B Bottom B SURFACE AREA (INCLUDES TOP & BOTTOM) SOMETIMES CALLED TOTAL AREA SA = LA + 2B Lateral Area LA

BASE AREA ( B ) TELLS THE NUMBER OF CUBES NEEDED TO FILL THE BASE THE HEIGHT ( h ) TELLS THE NUMBER OF LAYERS OF CUBES VOLUME VOLUME (How Much It Will Hold ) VOL = Bh

LATERAL AREA (SIDES OR LABEL ) LA = Ph SURFACE AREA (INCLUDES TOP and BOTTOM SOMETIMES CALLED TOTAL AREA) SA = LA + 2B VOLUME (HOW MUCH IT WILL HOLD) VOL = Bh

4 3 7 PRISM ( find P and B first ) l = 4 w = 3 h = 7 l = 4 w = 3 h = 7 P = = 14 P = = 14 B = 4 x 3 = 12 B = 4 x 3 = 12 LA = Ph = 14 x 7 = 98 sq units SA = LA + 2B = = 122 sq units Vol = Bh = 12 x 7 = 84 cubic units

r = 3 r = 3 h = 6 h = 6 P = 2πr = 6π P = 2πr = 6π B = πr² = 9π B = πr² = 9π LA = Ph = 6π x 6 = 36π sq units SA = LA + 2B = 36π + 18π = 54π sq u N VOL = Bh = 9π x 6 = 54π cu units CYLINDER63

CONES PYRIMIDS AND

PARTS OF A PYRIMID ( SQUARE BASE ) BASE EDGE HEIGHT ( h ) SLANT HEIGHT ( l )

PARTS OF CONES HEIGHT ( h ) r SLANT HEIGHT ( l )

LA = ½ P l SA = LA + B VOL= ⅓ B h

FIND THE PERIMETER AND AREA FIRST AND AREA FIRST 12 Base edge h sl P = = 48 B = 12 x 12 = 144 LA = ½ P l = ½ x 48 x 10 = 240 sq un SA = LA + B = = 384 sq un VOL = ⅓ B x h = ⅓ 144 x 8 = 384 cu un

3 r h sl P = 2 π r = 2 π 3 = 6 π B = π r² = 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