Warm Up Find the surface area and the

Warm Up Find the surface area and the volume 1. A prism with a length of 8 cm, width of 6 cm and height of 15 cm SA = 516 cm 2 V = 720 cm 3 2. A cylinder with a radius of 12 inches and a height of 20 inches SA = 2412. 7 in 2 V = 9047. 8 in 3

Surface Areas and Volumes of Pyramids and Cones

Pyramids • The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. • The height of a pyramid is the perpendicular segment from the vertex to the plane of the base.

Lateral and Surface Areas of Pyramids • The lateral faces of a regular pyramid create four identical triangles with a base of s and a height equal to the slant height of the pyramid. • LA = 2 sl • SA = s 2+ 2 sl

Example: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary. LA = 700 cm 2 SA = 896 cm 2

Example: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area the pyramid below: LA = 1600 cm 2 SA = 2225 cm 2

Lateral and Surface Areas of Cones • The slant height of a right cone is the distance from the vertex of a right cone to a point on the edge of the base. • The height of a cone is a perpendicular segment from the vertex of the cone to the plane of the base.

Lateral and Surface Areas of Cones • LA = πrl • SA = πr 2 + πrl

Example: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of the cone when: h = 12 cm, r = 9 cm and L = 15 cm. LA = 424. 1 cm 2 SA = 678. 6 cm 2

Example: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of the cone.

Volume of Pyramids and Cones

Example: Finding Lateral Area and Surface Area of Right Cones Find the volume of the cone when: h = 12 cm, r = 9 cm and L = 15 cm.

Example: Finding Volumes of Pyramids Find the volume of the square pyramid with base edge length 9 cm and height 14 cm.

Example: Finding Volumes of Pyramids Find the volume of the pyramid.

Example: Finding Volumes of Cones

Lesson Quiz: Find the volume of each figure. Round to the nearest tenth, if necessary. 1. a rectangular prism with length 25 cm, 3 width 17 cm, and height 21 cm V = 8925 cm 2. a cone with diameter 22 cm and height 30 cm V = 3801. 3 cm 3 3. a cone with base circumference 8 m and a height of 7 m V = 117. 3 3 4. a square pyramid with a base side length of 12 m and a height of 15 m V = 720 m 3