Review 2/28: Surface Area of Prisms (and Cylinders!)

p

4/30 Surface Areas of Pyramids and Conesp Pyramid: Polyhedron in which one face

(the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex.

p You name a pyramid by the shape of its base (triangular pyramid, rectangular pyramid, etc)

Learning Target: I can derive the formula for the surface area of a pyramid by using the perimeter of the base.

Surface Areas of Pyramids and Conesp The “height” of a pyramid is

perpendicular to the base (we will mostly use this next week for Volume.)

p The “slant height” h (often written “ l ”) is the height of one of the lateral faces (use this one for Surface Area!!)

**MUST BE IN NOTES!**

Net of a Pyramid

bh

Derivation: Prism à Pyramidp

2 2

**MUST BE IN NOTES!**

Surface Area of a Pyramidp Lateral Area: ½phn p = perimeter of the basen h = slant height (or lateral height

p Total Surface Area: B + ½phn p = perimeter of the basen h = slant height (or lateral height)n B = Area of the base

Surface Area of a Pyramidp Find the Surface Area of the Pyramid

12in

11in

S.A. = ½pl + BS.A. = ½(48)(11) + (144)

S.A. = 264 + 144S.A. = 408in2

What is the lateral area?L.A. = 264in2

What is the base area?B.A. = 144in2

Surface Area of Conesp Cone: “pointed” like a

pyramid, but its base is a circle

p The height is a segment from the vertex that is perpendicular to the base

p The slant height is the “height” of the side of the cone

Net of Cone

r

h

Derivation: Cylinders à Conesp

2 2

**MUST BE IN NOTES!**

Surface Area of a Conep Lateral Area: πrhn r = radiusn h = lateral height

p Surface Area: πr2 +πrh n r = radiusn h = lateral height

Surface Area of a Conep Find the Surface Area of the cone:

15cm

25cm

S.A. = �rl + �r2

S.A. = �(15)(25) + �(15)2

S.A. = 375 �+ 225 �S.A. = 600 � cm2 or 1884 cm2

What is the lateral area?L.A. = 375π cm2

HW Due 5/1: Pyramid and Cones Worksheet (Pick 3 on both pages)

Finding Slant Heightp Use Pythagorean Theorem!n �� + �� = ��

n Where “c” is your slant height

9 cm

8 cm

HW Due Monday 5/4p Pyramids and Cones Worksheet – Pick 3

from both sides