derive formulas of surface area – right prisms and right cylinders

Derive Formulas of Surface Area – Right Prisms and Right

Cylinders

Definition of a Prism

A Prism is a solid having bases or ends that are parallel, congruent polygons and sides that are parallelograms.

http://dictionary.reference.com/browse/prism

Parts of a Right PrismThe bases are congruent and parallel

The lateral faces are the faces connecting the corresponding vertices of the bases

Lateral edges are the segments connecting the lateral faces

Different Right Prisms

All Prisms with a Right angle

Oblique PrismA prism that has lateral edges that are not

perpendicular to the bases.

Height vs. Slant Height

A way to show the surface of a Prism

A two Dimensional representation of a prism is called a net

H

W

H

L

W

Another way is adding all the faces and bases

The equation

S.A. = 2(W·H + W·L + H·L)

W = 4; L = 7; H = 5

166832..

3528202..

7574542..

AS

AS

AS

To find surface area of a rectangular prism

S.A. = 2(2 x 4) + 2(3 x 4) + 2(2 x 3)

S.A. = 2(8) + 2(12) + 2(6)

S.A. = 16+ 24+ 12

S.A. = 52

Let’s Derive Surface Area Prism

SA = 2lw + 2wh + 2lhSA = 2lw + h(2w + 2l)SA = 2 bases + h perimeter⋅

HPBAS 2..

Surface Area of a Right Prism Theorem 12.2

The Surface Area of a Prism is the sum of two base areas and the lateral face areas.

Lateral faces = Height times Perimeter

B is area of a base

P is perimeter of the base

H is height

HPBAS 2..

Right Prism Theorem

The Base is 4(7)= 28

Perimeter is 2(4)+2(7) = 22

Height is 5

S.A. = 2(28) + 22(5)

S.A. = 166

HPBAS 2..

Your Turn!!!• Find the surface area

The bases are 12x2

S.A. = 2B+PhS.A. = 2(12x2) + 28x7S.A. = 48+196S.A. =244 cm2

Perimeter = 24 + 4H= 7

The bases are (11x17)/2

Perimeter = 11 +17 +20H = 6

S.A. = 2B+PhS.A. = 2(11x17)/2+ 48x6S.A. = 187+ 288S.A. =475 cm2

Define of a Cylinder

A Prism with a circular base

The net of a Cylinder

Two circles and a Rectangle

The Surface Area of a Cylinder

2 Bases + Circumference times height

HCBAS 2..

12

42

4 2

H

C

Base

The Surface Area of a Cylinder2 Bases + Circumference times height

HCBAS 2..

12

42

4 2

H

C

Base

128..

9632..

128162..

AS

AS

AS

hrrAS 22.. 2