SOLUTION: I need to find the surface area of a christmas tree I made for my summer project. The cone shape is 22 inches tall and has a diameter of 7.5 inches. There is also a base for the c

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Question 154402: I need to find the surface area of a christmas tree I made for my summer project. The cone shape is 22 inches tall and has a diameter of 7.5 inches. There is also a base for the cone shape. I also have a cylinder shape for the tree trunk wich is 3 inches in diameter and 5 inches in height. Please show me the calculations. I am using 2TTR(R+H) for both shapes but I do not think it is right and then I am not sure how to do the base of the cone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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I need to find the surface area of a Christmas tree I made for my summer project. The cone shape is 22 inches tall and has a diameter of 7.5 inches. There is also a base for the cone shape. I also have a cylinder shape for the tree trunk which is 3 inches in diameter and 5 inches in height. Please show me the calculations. I am using 2TTR(R+H) for both shapes but I do not think it is right and then I am not sure how to do the base of the cone.
:
First just find the surface area of the cone
The formula for that: SA = pi%2Ar%5E2 + pi%2Ar%2Al
:
In your problem r = 3.75 (half the diameter),
:
l is the slanted distance of the cone,
that will be the hypotenuse of a triangle formed by r and h
l = sqrt%283.75%5E2+%2B+22%5E2%29
l = 22.3173 inches
;
SA = pi%2A3.75%5E2 + pi%2A3.75%2A22.3173
SA = 44.1786 + 262.9195
SA = 307.0981 sq inches
:
Add the trunk: pi%2Ad+%2A+h
Trunk = pi%2A3%2A5
Trunk = 47.1239
:
Total; 307.0981 + 47.1239 = 354.222 sq/in (this includes the circular surface area of the bottom of the trunk)