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sonofjohn
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I hope I got 8 and 9 right. I am however stuck on 10. I can't seem to figure out how to convert x or a side to perimeter and represent the change in area with respect to time.
HallsofIvy said:You could get the exact change in volume by calculating the volume at r= 10.02 and r= 10 and subtracting but that is not what is asked.
You could do it either by setting r= 10, dr= 0.02 or by setting r= 10.02, dr= -0.02. You will get different answers but this only an "approximation". It is far easier to use r= 10, dr= 0.02.
Yes, that's the right answer (to 3 decimal places). Yes, 10 is the original radius, and dr = .02, both of which you need to find the change in volume.sonofjohn said:Alright thanks, I think I have a further understanding of this now. I did actually when I first started the problem, plug 10 and 10.02 into get the change in volume. Of course that wasn't an available answer and it wasn't the "approximate" answer. But after taking the derivative of the sphere volume formula with respect to radius I yield
dV\dr = 4pi(r)^2
I then plug in the radius 10 and the change in the radius .02.
dV/.02 = 4pi(10)^2
Finally,
dV = 25.133
Also Is there a reason I use 10 instead of 10.02? Is it because 10 was the original radius and we add .02 to the radius to find the change?
The formula for finding the area of a square is length multiplied by width. In the case of a square, the length and width are the same, so the formula is length x length or length².
To calculate the area of a square with a side length of 8, you would use the formula length x length or 8 x 8 = 64. The area would be 64 square units.
Perimeter is the distance around the outside of a shape, while area is the measure of the space inside a shape. In terms of a square, perimeter would be the measurement of all four sides added together, while area would be the measurement of the inside space of the square.
To find the area of a square with a diagonal length of 9, you would first need to find the length of one of the sides. Using the Pythagorean theorem, you can calculate that the length of one side is approximately 6.36. Then, using the formula length x length or 6.36 x 6.36 = 40.5696, the area of the square would be approximately 40.57 square units.
The area of a square with a perimeter of 10 cannot be determined without knowing the length of at least one of the sides. This is because different combinations of side lengths can have the same perimeter, but different areas. For example, a square with a perimeter of 10 could have sides of length 2.5, resulting in an area of 6.25, or sides of length 1, resulting in an area of 1. Therefore, the area cannot be determined with just the perimeter given.