Surface Area of Pyramid and Cone
Q1. First, let' set the faces=4 and click the net view. What shapes are the net of the pyramid consist of?
1xSquare (the base) and 4xtriangles (the lateral faces)
Q2. What is the relationship between the area of the net of pyramid and its surface area?
Same
Q3. What information do we need to find the area of the base? What information do we need to find the area of the lateral faces?
Side length (a) ; slant height (l) and side length (a)
Q4. Can you write a formula for the surface area of a sqaure pyramid?
SA=LA+A=4x (1/2al)+a[math]^2[/math]=2al+a[math]^2[/math]
[b]Now, let's look at the cone.[/b]
Q5.
What is the net of the cone consist of?
A circle (base) and a curved section (lateral face)
[b]Then, let's find out how to measure the area of the curved section.[/b]
Q6.
How can we approximate the area of the curved section, and what shape does the curved section tend to?
Divide the curved area into sections, then rearrange the sectors into a shape similar to a parallelogram.
Q7. What information do we need to find the area of the curved section?
Base (πr) and height (l)
Q8. What is the area of the curved section?
πrl
Q9.
What is the surface area of the cone?
SA=LA+A=πrl+πr[math]^2[/math]
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Information: Surface Area of Pyramid and Cone