review 2/28: surface area of prisms (and...
TRANSCRIPT
![Page 1: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/1.jpg)
Review 2/28: Surface Area of Prisms (and Cylinders!)
p
![Page 2: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/2.jpg)
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.
![Page 3: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/3.jpg)
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!**
![Page 4: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/4.jpg)
Net of a Pyramid
bh
![Page 5: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/5.jpg)
Derivation: Prism à Pyramidp
2 2
**MUST BE IN NOTES!**
![Page 6: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/6.jpg)
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
![Page 7: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/7.jpg)
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
![Page 8: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/8.jpg)
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
![Page 9: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/9.jpg)
Net of Cone
r
h
![Page 10: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/10.jpg)
Derivation: Cylinders à Conesp
2 2
**MUST BE IN NOTES!**
![Page 11: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/11.jpg)
Surface Area of a Conep Lateral Area: πrhn r = radiusn h = lateral height
p Surface Area: πr2 +πrh n r = radiusn h = lateral height
![Page 12: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/12.jpg)
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)
![Page 13: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/13.jpg)
Finding Slant Heightp Use Pythagorean Theorem!n �� + �� = ��
n Where “c” is your slant height
9 cm
8 cm
![Page 14: Review 2/28: Surface Area of Prisms (and Cylinders!)uprepgeometry.weebly.com/uploads/2/3/1/9/23192890/... · Review 2/28: Surface Area of Prisms (and Cylinders!) p. 4/30 Surface Areas](https://reader034.vdocuments.us/reader034/viewer/2022043013/5faedc89664b3c6b37344244/html5/thumbnails/14.jpg)
HW Due Monday 5/4p Pyramids and Cones Worksheet – Pick 3
from both sides