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GEOMETRY 3D solid. SURFACE AREA. SOLID SHAPES AND THEIR FACES. SOLID FIGURE Enclose a part of space. COMPOSITE SOLID It is made by combining two or more solids. SOLID FIGURES. RECTANGULAR PRISM Will slide and stack. Faces of a rectangular prism. SOLID FIGURES.
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GEOMETRY 3D solid SURFACE AREA
SOLID SHAPES AND THEIR FACES SOLID FIGURE Enclose a part of space COMPOSITE SOLID It is made by combining two or more solids
SOLID FIGURES RECTANGULAR PRISMWill slide and stack • Faces of a rectangular prism
SOLID FIGURES CylinderWill roll, stack, and slide • Faces of a cylinder
SOLID FIGURES PyramidWill slide • Faces of a pyramid
SOLID FIGURES Cone Will roll and slide • Face of a cone
SOLID FIGURES CubeWill slide and stack • Face of a cube
SOLID FIGURES SPHEREWill roll
Surface Area What does it mean to you?, Does it have anything to do with what is in the inside of figure? Surface area is found by finding the area of all the sides and then adding those answers up. How will the answer be labeled? Units2 because it is area!
Surface Area Steps for Finding Surface Area 1. Draw and label each face of the solid as if you had cut the solid apart along its edges and laid it flat. Label the dimensions. 2. Calculate the area of each face. If some faces are identical, you only need to find the area of one. 3. Find the total area of all the faces.
PRISM In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms.
PRISM PYRAMID In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms. In a pyramid, the base can be any polygon. The lateral faces are triangles.
Top Back Side 2 Side 1 Front Bottom Rectangular Prism Top Back Side 2 Side 1 Front Bottom
Rectangular Prism Net H B H B H B B H H B H H B
Surface Area of a Prism Calculate the area of each face. If some faces are identical, you only need to find the area of one. Then, find the total area of all the faces. Example: Find the surface area of this rectangular prism It is made by: 2 congruent bases, and 4 lateral faces Surfacearea 180 m2 Base area = 2(6 x 8) = 96 m2 Lateral surfacearea (front and back) = 2 (3x6) = 36 m2 Lateral surfacearea (sides) = 2 (3x8) = 48 m2 Surfacearea = 96 + 36 + 48 = 180 m2
B C 5 in A 6 in 4 in Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. Do any of the faces have the same area? If so, which ones? Opposite faces are the same. Find the SA A = 5 x 4 = 20 x 2 = 40 B = 4 x 6 = 24 x 2 = 48 C = 6 x 5 = 30 x 2 = 60 Surface Area = 40 + 48 + 60 = 148 in2 Surface Area of a Rectangular Prism 2A + 2B + 2C
Triangular Prism How many faces are there? 5 5 4 10 m 3 How many of each shape does it take to make this prism? 2 triangles and 3 rectangles = SA of a triangular prism Find the area of the 3 rectangles. Find the area of the triangle. Front 5 x 10 = 50 Back 4 x 10 = 40 Botton 3 x 10 = 30 120 4 x 3/2 = 6 x 2 = 12 2 How many triangles were there? Area of bases + area of laterals = SA 12 + 120 = SA What is the final SA? SA = 132 m2
Cube Are all the faces the same? YES How many faces are there? 6 Find the Surface area of one of the faces. 4m 4 x 4 = 16 Take that times the number of faces. x 6 96 m2 SA for a cube. Surface Area of a Cube = 6 a 2
Surface Area of a cylinder • The two bases are circular regions, so you need to find the areas of two circles • The lateral surface is a rectangular region • The height of the rectangle is the height of the cylinder • The base of the rectangle is the circumference of the circular base Example: Find the surface area of the cylinder It is made by: 2 congruent circles, and 1 rectangle Circlearea= 3.14 (5)2 78.5 x 2 157 in2 Lateral area= (2 x 3.14 x 5 )12 376.8 in2 b= c = 2 r h= 12 Cylindersurfacearea = 157 + 376.8 = 533.8 in2
Cylinders 3 What does it take to make this? 2 circles and 1 rectangle = SA cylinder 10m 2B + LSA = SA Surface Area of a Cylinder 2 circles (bases) 1 rectangle (Lateral) SA = 56.52 + 188.4 SA = 244.52
CLASS WORK Find the surface area of each solid. All given measurements are in centimeters
PYRAMID In a pyramid, the base can be any polygon. The lateral faces are triangles.
PYRAMID SQUARE PYRAMID REGULAR N-GON PYRAMID Slant Height Altitude Slant Height Base Altitude Base
PYRAMID SQUARE PYRAMID
PYRAMID REGULAR N-GON PYRAMID
PYRAMID Slantheight : It ist he height of each triangular lateral face. Itislabeledl The pyramid height is labeled h. The surface area of a pyramid is the area of the base plus the areas of the triangular faces(lateral area). SA = L+B Surface Area Base Area Lateral Area
PYRAMID The surface area of a pyramid is the area of the base plus the areas of the triangular faces. What is the area of each lateral face? _1_bl 2 What is the total lateral surface area for any pyramidwith a regular n-gon base n . _1_bl 2 What is the area of the base for any regular n-gonpyramid? 1 aPor1 abn 2 2 The formula for the surface area of a regular n-gonpyramidin terms of n, base length b, slant height l, and apothem a. SA = 1 nb(l+a) 2
PYRAMID The expression for the surface area of a regular n-gon pyramid in terms of height l, apothema, and perimeter of the base, P. SA= 1 P(l+a) 2
PYRAMID The formulas to find the surface area of a pyramid are: SA = L+B Basic formula SA = 1 P(l+a) 2 SA = 1 nb(l+a) 2 or in terms of : n = number of triangular faces b = base length , l= slant heightand a = apothem in terms of : l = height, a = apothem, and , P = perimeter of the base.
Spheres • Sphere – The set of all points in space equidistant from a given point. Center Radius – Is a segment that has one end point at the center & the other end point on the sphere. r Diameter – A segment passing through the center w/ both end points on the sphere.
Spheres SA = 4r2 r Radius of a sphere
Spheres SA = 4r2 = 4(4)2 = 4(16) = 64 = 201.1m2 4m
CONES lateral surface l l r Base = πr2 lateral surface= πrl
CONES The surface area is the sum of the area of its base and the lateral (side) surface. l πr2 Find the area of the circle, or base Find the area of the curved (lateral) surface cone r πrl The surface area of the cone equals the area of the circle plus the surface area of the cone given by Where,r is the radiusl is the slant height