Warm Ups Find the surface area of the polyhedron...
Transcript of Warm Ups Find the surface area of the polyhedron...
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Warm Ups
Find the surface area of the polyhedron below.
4 in4 in
8 in
Homework Solutions/Questions
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Learning Objectives
• I can calculate the surface area of a cylinder.• I can calculate the surface area of a cone.• I can calculate the surface area of a sphere.• I can correctly label answers with the proper unit (cm, cm2, or cm3).
Success Criteria
6. A hemisphere has a radius of 10 m. Find the surface area (don't forget the bottom).
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Polyhedra vs. Non-polyhedra
Polyhdron (polyhedra): a 3D solid with flat polygonal faces Examples: prisms, pyramids
Nonpolyhedron (nonpolyhedra): a solid with non-polygonal faces Examples: today's lesson :)
Oblique vs. Right: we can only find the surface area of right solids
Surface Area of Cylinders
10 cm
25 cm
We are still going to use our "formula" from yesterday to find surface area (a.k.a. add up all the faces)
1. Find the surface area of the cylinder.
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Surface Area Formulas
10 cm
25 cm
Let's try to generalize what we did...
2πr
h
πr2
πr2
Surface Area Formulas
10 cm
25 cm
Let's try to generalize what we did...
2πr
h
πr2
πr2
2πrh
Surface Area of a Cylinder = 2πr2 + 2πrh
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
l
r
Surface Area Formulas
Surface Area of a Cone = πr2 + πrl
h
r
l
l = lateral height (slant)
Surface Area Formulas
Surface Area of a Sphere = 4πr2
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Surface Area of Cylinders
2. Find the surface area of a cylinder that has a diameter of 4 cm and a height of 10 cm.
Surface Area of Cones
3. Find the surface area of the cone.
12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017
Surface Area of Spheres
4. Find the surface area in terms of π.
Surface Area of Cones
5. The surface area of a cone is 900 mm2 and it has a radius of 12 mm. Find the lateral height.