Great video! I don't think the math makes sense though - should calculate area covered by each hotspot (pi * radius^2) and divide total area (40*25) by area per hotspot to get number of hotspots (approx 13) and multiple by cost to get $13M
With all due respect, how did you come to 27 hotspots ? Isn’t dividing area of the rectangle by the area of one circle going to cover all the area? I understand it being a circle means having a few open spots but covering those would be an additional 7 hotspots, bringing us to a total of 20 hotspots (13 + 7).
I also got 27 hotspots. The secret is to draw out. Think of 8 golf balls, 5 cm radius each, tightly positioned from the top in the 40 cm x 25 cm gift box. You are basically covering up so that you cannot see any crevice from the sky. You will find 5 x 3 holes between the balls themselves and the balls and corners. You also need to add 4 more on the bottom, below each ball because there are 5 cm gaps. Therefore, you need 8 + 15 + 4 balls so that there is no black space from the helicopter view.
Actually 24 hotspots is enough, find a square in the circle which is approximately 7 x 7, you need 6 of it to cover the 40 unit wide (total to 42), and 4 to cover 25 unit height (total to 28). So 24 is sufficient How calculate the units of square in the circle, draw two radius 90 degree to each other, connects them and you will get the length of one side of the circle. Which is the square roots of 50, around 7 units. Hope this helps
@@varadajitkshirsagar6880 I think the best way to approach the math is to consider the biggest square that can fit into a circle. This square will have a diagonal of 10 units. that means that the square has a side of root square 50 or the square has an area of 50. Finally, we can divide the total area (40x25)/50=20
The best solution is to look for the biggest square circumscribed in a circle of radius 5. Then divide 40 into the length of that area, same with 25. Finally, multiply both results. From Pitagoras theorem, one can get 2*a=2*sqrt(c^2 /2) Where “c” is the radius of the circle, and “2*a” is the length of the square side. Replacing c=5 results in 10*sqrt(0.5) ≈ 7 Then 40/7=5.71≈6 25/7= 3.57≈4 But values must be rounded up. Then the final answer is 6*4=24
I would have done this differently. Square area = 40x25=1000 sq ft. Circular area per hotspot = pi x r^2 = (3)(5)(5) = 75. Therefore you need at least 1000/75 = at least ~15 hotspots + some buffer for inevitable overlap
Hi there, Thanks for making such a awesome video for us. Just a quick question, how long we can think of the clarifying questions? Is there any way we could speed up?
I think the way he went about is: 1. For a circle to compensate for the overlaps, consider them as square with the diameter as the diagonal of it. 2. With that (although I am not sure he did it that way) you can estimate the side of the square. i.e 10/sqrt (2). 3. Then you just calculate the number of squares that will be needed to fill the area of 40*25 units. Round off the sqrt (2) to 1.5 to make calc easier. Ballpark it's going to be around 28. Hope this helps.
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Great video! I don't think the math makes sense though - should calculate area covered by each hotspot (pi * radius^2) and divide total area (40*25) by area per hotspot to get number of hotspots (approx 13) and multiple by cost to get $13M
you cant do that. its a circle. i got 27 hotspots to cover the area.
With all due respect, how did you come to 27 hotspots ? Isn’t dividing area of the rectangle by the area of one circle going to cover all the area? I understand it being a circle means having a few open spots but covering those would be an additional 7 hotspots, bringing us to a total of 20 hotspots (13 + 7).
I also got 27 hotspots. The secret is to draw out. Think of 8 golf balls, 5 cm radius each, tightly positioned from the top in the 40 cm x 25 cm gift box. You are basically covering up so that you cannot see any crevice from the sky. You will find 5 x 3 holes between the balls themselves and the balls and corners. You also need to add 4 more on the bottom, below each ball because there are 5 cm gaps. Therefore, you need 8 + 15 + 4 balls so that there is no black space from the helicopter view.
Actually 24 hotspots is enough, find a square in the circle which is approximately 7 x 7, you need 6 of it to cover the 40 unit wide (total to 42), and 4 to cover 25 unit height (total to 28). So 24 is sufficient
How calculate the units of square in the circle, draw two radius 90 degree to each other, connects them and you will get the length of one side of the circle. Which is the square roots of 50, around 7 units. Hope this helps
@@varadajitkshirsagar6880 I think the best way to approach the math is to consider the biggest square that can fit into a circle. This square will have a diagonal of 10 units. that means that the square has a side of root square 50 or the square has an area of 50. Finally, we can divide the total area (40x25)/50=20
The best solution is to look for the biggest square circumscribed in a circle of radius 5. Then divide 40 into the length of that area, same with 25. Finally, multiply both results.
From Pitagoras theorem, one can get 2*a=2*sqrt(c^2 /2)
Where “c” is the radius of the circle, and “2*a” is the length of the square side.
Replacing c=5 results in 10*sqrt(0.5) ≈ 7
Then 40/7=5.71≈6
25/7= 3.57≈4
But values must be rounded up.
Then the final answer is 6*4=24
I would have done this differently. Square area = 40x25=1000 sq ft. Circular area per hotspot = pi x r^2 = (3)(5)(5) = 75. Therefore you need at least 1000/75 = at least ~15 hotspots + some buffer for inevitable overlap
this would not include overlaps so this answer is wrong
Didn't really get the process of solving the math question. Has anybody got that?
I don’t think he followed any structure, he was just giving launder list
Hi there, Thanks for making such a awesome video for us. Just a quick question, how long we can think of the clarifying questions? Is there any way we could speed up?
is there a clearer way to break down the math
Hi...can you (anyone) please explain the maths process (calculations)?
I think the way he went about is: 1. For a circle to compensate for the overlaps, consider them as square with the diameter as the diagonal of it.
2. With that (although I am not sure he did it that way) you can estimate the side of the square. i.e 10/sqrt (2).
3. Then you just calculate the number of squares that will be needed to fill the area of 40*25 units. Round off the sqrt (2) to 1.5 to make calc easier. Ballpark it's going to be around 28.
Hope this helps.