PRISMS

PARTS of a PRISM

BASE

FACE

HEIGHT

BASE

FACE

HEIGHT

TOTAL SURFACE AREA

The sum of the areas of each face.

T.A. = ph + 2B

p = perimeter of the base

h = height of the prism

VOLUME of a PRISM

V = BhB = area of the Base

h = height of the prism

A right triangular prism is shown. Find the total surface area since the volume = 315.

h

7 6.54

10.5 T.A. = T.A. = phph + 2B + 2BV= Bh = 315V= Bh = 315

V= (V= (½·10.5·4)½·10.5·4)h = h = 315315V= 21h = V= 21h = 315315 h = 15h = 15

p = 10.5 + 7 + 6.5p = 10.5 + 7 + 6.5h = 15h = 15

B =B =½·10.5·4 = 21½·10.5·4 = 21

T.A. = T.A. = 24(15) + 24(15) + 2(21)2(21)T.A. = T.A. = 402402

Parts of a Pyramid

SLANT HEIGHT

The height of the isosceles triangular lateral face

Examples of Pyramids

SLANT HEIGHT

TOTAL SURFACE AREA

T.A. = ½pl + B

p= perimeter of the base

l = slant height

B = area of the base

VOLUME of a Pyramid

V = ⅓Bh

B = Area of the base

h = height of the pyramid

Find the total surface area and volume of the pyramid.

25 m

24 m 20 m

T.A. = T.A. = ½½pl pl + B+ B p = 14(4) = 56p = 14(4) = 56 l = 24l = 24 B = 14 (14) = 196B = 14 (14) = 196

T.A. = T.A. = ½½(56)(24) (56)(24) + 196 = + 196 = 868868

V = ⅓BhV = ⅓Bh

B = 14(14) = 196B = 14(14) = 196

h = 20h = 20

V = ⅓BhV = ⅓Bh⅓⅓(196)(20)(196)(20)1306.666661306.66666

CylindersBase is always a circle

Parts of a CYLINDER

TOTAL SURFACE AREA

T.A. = 2пrh + 2B

r = radius of the base

h = height of the cylinder

B= area of the base

VOLUME of a Cylinder

V = пr2h

r = radius of the base

h = height of the cylinder

Find the total surface area and volume.

7 in

24 in

T.A. = 2T.A. = 2ппrhrh + 2B + 2B

h = 24h = 24

r = 7r = 7

B = B = ππrr22 = = ππ(7)(7)22 = 49πT.A. = T.A. = 22ππ(7)(24) +(7)(24) + 2(49π)

T.A. = T.A. = 336336ππ + + 98π = 434π

V = V = ππr r 22hh

V = V = ππ(7) (7) 2 2 (24)(24)

V = 1176 V = 1176 ππ

CONES

TOTAL SURFACE AREA

T.A. = пrl + B

r = radius of the base

l = slant height of the cone

B= area of the base

VOLUME of a Cone

V = ⅓пr2h

r = radius of the base

h = height of the cone

Find the total surface area and volume.

16 meters

17 meters

T.A. =T.A. = ππrl rl + B+ B

T.A. = T.A. = ππ(8)(17) + (8)(17) + 6464ππ

B = 8B = 82 2 ππ = = 6464ππ

T.A. = 136T.A. = 136ππ + 64 + 64ππT.A. =T.A. = 200200ππ

V = ⅓V = ⅓ππrr22hh

V = V = ⅓⅓ππ((8822)15)15V = 320V = 320ππ

Spheres

TOTAL AREA

T.A. = 4пr2

r = radius of the sphere

VOLUME of a Sphere

V = 4/3 пr3

r = radius of the sphere

A basketball has a diameter of about 9 inches. What is the total area and volume of the basketball?

T.A. = 4T.A. = 4ππrr22

T.A. = 4T.A. = 4ππ(9/2)(9/2)22

T.A. = T.A. = 8181ππV = 4/3 V = 4/3 ππrr33

V = 4/3 V = 4/3 ππ(9/2)(9/2)33

V = 121.5V = 121.5ππ