Hello, I am trying to figure out the radius of this convex curve on my pool that I plan to put a waterfall on. Did I do this measurement correctly? Please see photos?
Thanks
Thanks
Radius of a convex curve for a waterfall
- Thread starter poolremodelnewbie
- Start date
(((11.083^2)÷(4 x 2.67)) + 2.67) ÷ 2 =7.08
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Note that 2'8" is 2.667 feet and 11'1" is 11.083 feet.
radius circle chord length 11.08 chord height 2.67 - Wolfram|Alpha
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Note that 2'8" is 2.667 feet and 11'1" is 11.083 feet.
Method 1:
(((11.0833^2)÷(4 x 2.667)) + 2.667) ÷ 2 =7.0908837125
Method 2:
(r – 2.667)^2 + (5.541)^2 = r^2
((-2.667)^2 + (5.541)^2) ÷ (2 x 2.667) = 7.089533
Method 3 ask wolframalpha
www.wolframalpha.com
Answer = 7.09057
Method 4
(2.667 ÷ 2) + ((11.083^2) ÷(8 x 2.667)) = 7.09057 feet (7'1").
Note that you should be able to verify the diameter of 14.18 feet (14'2") by holding a tape measure at one side of the circle and moving the other side until you find the farthest spot on the opposite side.
(((11.0833^2)÷(4 x 2.667)) + 2.667) ÷ 2 =7.0908837125
Method 2:
(r – 2.667)^2 + (5.541)^2 = r^2
((-2.667)^2 + (5.541)^2) ÷ (2 x 2.667) = 7.089533
Method 3 ask wolframalpha
radius circle chord length 11.083 chord height 2.667 - Wolfram|Alpha
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
www.wolframalpha.com
Answer = 7.09057
Method 4
(2.667 ÷ 2) + ((11.083^2) ÷(8 x 2.667)) = 7.09057 feet (7'1").
Note that you should be able to verify the diameter of 14.18 feet (14'2") by holding a tape measure at one side of the circle and moving the other side until you find the farthest spot on the opposite side.
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Yes when i continue the height measurement to the other side of the circle it is about 14 ft 2 in approx.Method 1:
(((11.0833^2)÷(4 x 2.667)) + 2.667) ÷ 2 =7.0908837125
Method 2:
(r – 2.667)^2 + (5.541)^2 = r^2
((-2.667)^2 + (5.541)^2) ÷ (2 x 2.667) = 7.089533
Method 3 ask wolframalpha
radius circle chord length 11.083 chord height 2.667 - Wolfram|Alpha
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
Answer = 7.09057
Method 4
(2.667 ÷ 2) + ((11.083^2) ÷(8 x 2.667)) = 7.09057 feet (7'1").
Note that you should be able to verify the diameter of 14.18 feet (14'2") by holding a tape measure at one side of the circle and moving the other side until you find the farthest spot on the opposite side.
Thank you very much!
Sparks22
Gold Supporter
That's too easy. Much more fun to do the math. Anytime you can break out the geometry, calculus, or differential equations is a good day.
Also, maybe the tape measure was only 12 feet long and couldn't reach the entire diameter.
I have actually invented an elastic tape measure that will stretch up to 50% for just such a case where the tape measure is a little bit too short. However, I can't find anyone to invest in producing it.
Also, sometimes you don't have a full circle where you can check the diameter.
If you have less than a half circle, you have to use a mathematical method.
If you have a full circle you could measure the circumference and figure out the radius from that.
For a radius of 7.09057 feet, the circumference should be 44.5514 feet. (Formula Circumference = 2πr)
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