The cone shown has a radius of 5 feet and a slant height of 12 feet. Which choice is closest to the total surface area? Use 3.14
2 answers:
So first of all, to solve this, we need to know the formula for finding the surface area of a cone. The formula is :
Where SA stands for surface area, h stands for height, and r stands for radius.
In the given information, we are not told the height, but we are told the slant height.
In a cone, the slant height, the height, and the radius together form a right triangle. We can use that triangle to solve for the height
So, to find the height, we can do:
5^2+b^2 = 12^2, or 25+b^2 = 144
Therefore, b is equal to about 11
So now, we can plug all of our values into the formula
This gives us:
If we solve, this gives us about 267.
Therefore the answer is 267 feet squared
Hope this helped!! :D
Where SA stands for surface area, h stands for height, and r stands for radius.
In the given information, we are not told the height, but we are told the slant height.
In a cone, the slant height, the height, and the radius together form a right triangle. We can use that triangle to solve for the height
So, to find the height, we can do:
5^2+b^2 = 12^2, or 25+b^2 = 144
Therefore, b is equal to about 11
So now, we can plug all of our values into the formula
This gives us:
If we solve, this gives us about 267.
Therefore the answer is 267 feet squared
Hope this helped!! :D
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Check the picture below.
now, you can pretty much count the units off the grid for the segments ST and RU, so each is 7 units long, and are parallel, meaning that the other two segments are also parallel, and therefore the same length each.
so we can just find the length for hmmmm say SR, since SR = TU, TU is the same length,
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{-5}~,~\stackrel{y_2}{5})\qquad \qquad % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ SR=\sqrt{[-5-(-2)]^2+[5-1]^2}\implies SR=\sqrt{(-5+2)^2+(5-1)^2} \\\\\\ SR=\sqrt{(-3)^2+4^2}\implies SR=\sqrt{25}\implies SR=5](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0AS%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%0AR%28%5Cstackrel%7Bx_2%7D%7B-5%7D~%2C~%5Cstackrel%7By_2%7D%7B5%7D%29%5Cqquad%20%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%5B-5-%28-2%29%5D%5E2%2B%5B5-1%5D%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B%28-5%2B2%29%5E2%2B%285-1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%28-3%29%5E2%2B4%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B25%7D%5Cimplies%20SR%3D5)
sum all segments up, and that's perimeter.
now, you can pretty much count the units off the grid for the segments ST and RU, so each is 7 units long, and are parallel, meaning that the other two segments are also parallel, and therefore the same length each.
so we can just find the length for hmmmm say SR, since SR = TU, TU is the same length,
sum all segments up, and that's perimeter.