3.2a: surface area of prisms and cylinders p. 591-598 primary m(g&m)–10–6 solves problems...
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3.2a: Surface Area of Prisms and Cylinders
p. 591-598
Primary
M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three
SecondaryM(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)
3-D figures- Solid figures. When the sides are polygons, its called a polyhedron.
Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent 2) lateral faces that are parallelograms
Base
Base (parallel & Congruent)
Altitude (height)- Distance between the bases
Lateral Face – parallel sides not the base
Lateral Edge
* names by the shape of their bases
Areas of the Solids
Lateral Area (LA) – the sum of the areas of the lateral faces only.
– Does not include the area of the bases.
Surface Area (SA) – the sum of the areas of ALL the faces.
– Lateral area + area of the bases
Lateral Area of a Right Prism
PhLAP = Perimeter of the base
h= height between the bases (altitude)
Surface Area of a Right Prism
BPhSA 2B = Area of one Base
Ex: Find the lateral & surface areas of the triangular prism.
LA = Ph
P = 6*3 = 18
LA = 18*10
LA = 180 in2
S = 2B + Ph
S = 2(15.59) + 180
S = 31.18 + 180
S = 211.18 in2
6 in
.
10 i
n.
4
32sB
4
336 39 59.15
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http://guilford.rps205.com/departments/Math/Links/Honors%20Geometry/Honors%20Geometry%20Power%20Points/12.2%20SA%20of%20Prisms%20&%20Cylinders.ppt#7
Find the Surface Area
Find the lateral and surface areaOf the regular pentagonal prism
10 ft
Cylinders: 1) has 2 circular bases 2) bases are both parallel and congruent
Right cylinder – the axis is the same as the altitude
Oblique Cylinder-The axis is longer than the altitude
axisaltitude
Lateral Area of a Right Prism
ChLAC = circumference of the base circle
h= height between the bases (altitude)
Surface Area of a Right Prism
BChSA 2B = Area of one Base
Find the surface area and lateral area
Example
A right cylinder has a surface area of 400 square mm. Find the height of the cylinder if the diameter of the base of the cylinder is 10 mm.
example2
If the side of a cube is doubled, what happens to the surface area ?
Challenge
The Lateral Area of a right rectangular prism is 784 square cm.
Its length is three times its width.
Its height is twice its width.
Find the surface area.
A square with a side length of 8.0 cm is rolled up, without overlap, to form the lateral surface of a cylinder.
What is the radius of the cylinder to the nearest tenth of a centimeter?
Ex. 1 – Released Item from 2007 NECAP
Ex 2. Find the Surface Area
13 in
5 in
12 in
4 in
Homework
