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 cm2 V = 720 cm3 2. A cylinder with a radius of 12 inches and a height of 20 inches SA = 2412.7 in2 V = 9047.8 in3

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 = 2sl SA = s2+ 2sl

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. SA = 896 cm2 LA = 700 cm2

Example: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area the pyramid below: SA = 2225cm2 LA = 1600cm2

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 = πr2 + 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. SA = 678.6 cm2 LA = 424.1 cm2

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, width 17 cm, and height 21 cm 2. a cone with diameter 22 cm and height 30 cm 3. a cone with base circumference 8 m and a height of 7 m 4. a square pyramid with a base side length of 12 m and a height of 15 m V = 8925 cm3 V = 3801.3 cm3 V = 117.3 3 V = 720 m3