10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres Day 1 Warm-up

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1 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron has 7 vertices and 12 edges. Which number of faces justifies Euler s formula? A 3 C 17 B 7 D What best describes the cross section shown on the cube? A square C trapezoid B triangle D rectangle 4. In the figure, which number should be substituted for V in Euler s formula? A 6 C 12 B 8 D 18

2 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres PRISM: polyhedron with congruent two faces, called bases, that lie in parallel planes. (Prisms are classified by the shapes of their.) bases The other faces, called lateral faces, are parallelograms formed by connecting the corresponding vertices of the bases. The segments connecting these vertices are lateral edges. o Right prism: each lateral edge is perpendicular to both bases. o Oblique prism: the lateral edges are not to perpendicular the bases.

3 Lateral Area of a Prism: sum of the areas of the lateral faces SURFACE AREA of a Right Prism: sum of the areas of the two bases and the lateral area.. S.A. = 2B + Ph (B = area of a base, P = perimeter of a base, h = height of the prism)

4 Find the surface area of the right prism m 12 m

5 CYLINDER: solid with congruent circular bases that lie in parallel planes. o Right Cylinder: if the segment joining the centers of the bases is perpendicular to the bases.

6 Lateral Area of a Cylinder: the area of its curved surface. SURFACE AREA of a Right Cylinder: sum of the areas of the two bases and the lateral area S.A. = 2B + Ch (B = area of a base, C = circumference of a base, h = height of the cylinder) S.A. = 2πr 2 + 2πrh (r = radius of a base)

7 Find the surface area of the right cylinder

8 10.4 Day 2 Warm Up Write a description of each figure. 1. cube prism with 6 square faces 2. pentagonal prism prism with 2 pentagonal bases and 5 lateral faces that are parallelograms 3. cylinder figure with 2 circular bases connected by a curved surface

9 polygon PYRAMID: polyhedron in which the base is a and the lateral faces are triangles with a common vertex. (Pyramids are classified by the shape of their.) bases The intersection of two lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge. The altitude or height of the pyramid is the perpendicular distance between the base and the. vertex o Regular pyramid: has a regular polygon for a base and its height meets the base at its. center The slant height of a regular pyramid is the of lateral face. altitude any

10 SURFACE AREA of a Regular Pyramid: S.A. = B + ½ Pl (B = area of the base, P = perimeter of the base, l = slant height)

11 Find the surface area of the regular pyramid

12 CONE: has a circular base and a vertex that is not in the same plane as the base. The altitude or height is the perpendicular distance between the vertex and the. base The lateral surface of a cone consists of all segments that connect the vertex with the points on the base edge. Right Cone: the height meets the base at its. center The slant height is the distance between the vertex and a point of the base edge.

13 SURFACE AREA of a Right Cone: S.A. = B + ½ Cl (B = area of the base, C = circumference of the base, l = slant height) S.A. = πr 2 + πrl (r = radius of the base, l = slant height)

14 Find the surface area of the right cone

15 SPHERE: the of locus points in space that are a given distance from a. point The point is called the center of the sphere. A radius of a sphere is a segment from the center to a on point the sphere. A great circle is the cross section of a sphere with a plane that goes through the center of the sphere. Every great circle of a sphere separates the sphere into two congruent halves called hemispheres. SURFACE AREA OF A SPHERE: S.A. = 4πr 2 (r = radius of the sphere)

16 Find the surface area of the sphere

17 1. 2. Add to your notes All spheres are similar to each other. Use problems 1 and 2 above to answer the following. What is the ratio of their radii? What is the ratio of their surface areas? Given two spheres have radii with a ratio of a, what is the ratio of their surface areas? b

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