August 9, 2019 Write in your planner and on your stamp sheet: Homework: 11.12 WS WARM-UP: Write down each problem and solve. Show your thinking!

How do we find the surface area of any shape? We find the surface area of any shape by finding the area of all the surfaces. What are all the surfaces of a cylinder?

Net of a cylinder

Formula for Surface Area of a Cylinder Check out this website for a nice visual and explanation of surface area: http://www.mathopenref.com/cylinderarea.html

Net of a cylinder What are the different dimensions of a cylinder? Circumference = radius x 2 x pi Radius What are the different dimensions of a cylinder? The length of the rectangle is the same as the circumference. Area of rectangle = length x height of cylinder Height Based on this information, write a formula for solving for the surface area of a cylinder.

What is the formula for the Area of the Base (B): Name of shape:  Shape of Base: What is the formula for the Area of the Base (B): Find the area of the Base (B): How many Bases are there? Write a formula for finding the area of both Bases: Solve for the area of both Bases: Cylinder Circle Π x r² 3.14 x 5 x 5 = 78.5 Two 2 x Π x r² 2 x 3.14 x 5 x 5 = 157.08

We've got the 2 circles, now we need to find the area of the "curved surface" Check out this website for a nice visual and explanation of surface area: http://www.mathopenref.com/cylinderarea.html

Highlight the same lines on the cylinder. Highlight the top and bottom lines of the “curved surface” in Figure 2. Highlight the same lines on the cylinder. What is the name of the dimension you highlighted?   What is the formula for finding the distance of this dimension? Circumference Circumference : 2 x r x π

Find the distance of this dimension: Look at Figure 2. Do we know all of the dimensions of the “curved surface”? What is the formula for the area of the curved surface?   Solve for the area of the curved surface: Circumference : 2 x 5 x π = 31.4 2 x r x π x height 2 x 5 x π x 20 = 628.32

Now that you know the areas for all the faces, solve for the surface area of the cylinder:   In your own words, what do you need to know to find the surface area of a cylinder? Write a formula to explain this: 157.08+ 628.32= 785.4  (2 x π x r²) + (2 x r x π x h)

Formula for Surface Area of a Cylinder S.A. = radius x radius x pi x 2 + pi x radius x 2 x height This part of the formula solves for the area of the two circles. This part of the formula solves for the area of the rectangle.

Solve for Surface Area – Show your work! 28 in Radius = 28 in Surface Area = 28 x 28 x 3.14 x 2 + 28 x 2 x 3.14 x 60 Surface Area = 15481.77 square inches 60 in 10 m Diameter = 10 m Radius = 5 m Surface Area = 5 x 5 x 3.14 x 2 + 5 x 2 x 3.14 x 8 Surface Area = 408.41 square meters 8 m