Warm Ups Find the surface area of the polyhedron...

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12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017 Warm Ups Find the surface area of the polyhedron below. 4 in 4 in 8 in Homework Solutions/Questions

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.

12A.02+ Cylinders, Cones, and Spheres.notebook May 10, 2017

Success Criteria

6. A hemisphere has a radius of 10 m. Find the surface area (don't forget the bottom).