10 4 Surface Area of Pyramids and Cones

What is a pyramid? �A pyramid is a polyhedron in which one face (the

More about the pyramid: �A regular pyramid is a pyramid whose base is a

Lateral Area of a Pyramid: � The lateral area of a pyramid is the

Surface Area of a Pyramid: � The surface area of a regular pyramid is

Example 1: Surface area of a pyramid. � Find the surface area of the

Example 2: Real – World Connection � Social Studies The Great Pyramid at Giza,

What is a cone? �A cone is “pointed” like a pyramid, but its base

Lateral and Surface Area of a Cone � � The lateral area of a

Example 3: Finding surface area of a cone. � Find the surface are of

Example 4: Real-World Connection � Chemistry The funnel is in the shape of a

Homework: � Pg 540 – 541 #s 2 – 20 even, 25 – 27

Slides: 13

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10 -4 Surface Area of Pyramids and Cones L. E. Q. How do you find the surface areas of pyramids and cones?

What is a pyramid? �A pyramid is a 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 (called the vertex of the pyramid). � The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base and is the height of the pyramid.

More about the pyramid: �A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. � The slant height is the length of the altitude of a lateral face of the pyramid.

Lateral Area of a Pyramid: � The lateral area of a pyramid is the sum of the areas of the congruent lateral faces.

Surface Area of a Pyramid: � The surface area of a regular pyramid is the sum of the lateral area and the area of the base.

Example 1: Surface area of a pyramid. � Find the surface area of the hexagonal pyramid below.

Example 2: Real – World Connection � Social Studies The Great Pyramid at Giza, Egypt, pictured below, was built about 2580 B. C. as a final resting place for Pharaoh Khufu. At the time it was built, its height was about 481 ft. Each edge of the square base was about 756 ft long. What was the lateral area of the Great Pyramid?

What is a cone?

What is a cone? �A cone is “pointed” like a pyramid, but its base is a circle. � In a right cone the altitude is a perpendicular segment from the vertex to the center of the base. � The height h is the length of the altitude. � The slant height is the distance from the vertex to a point on the edge of the base.

Lateral and Surface Area of a Cone � � The lateral area of a right cone is half the product of the circumference of the base and the slant height. The surface area of a right cone is the sum of the lateral area and the area of the base.

Example 3: Finding surface area of a cone. � Find the surface are of the cone below in terms of pi.

Example 4: Real-World Connection � Chemistry The funnel is in the shape of a cone. How much filter paper do you need to line the funnel?

Homework: � Pg 540 – 541 #s 2 – 20 even, 25 – 27 all.