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Question 958125: If the radius of a circular solar cell is increased by a factor of 1.7, the area of the cell increases by 53
cm2
. Find the radius (in cm) of the new solar cell.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The formula for the area of a circle is A = pi * r^2.
We'll call that A1.
If the radius is increased by a factor of 1.7, then the new radius is equal to 1.7 * the old radius.
The formula for this new area becomes A2 = pi * (1.7 * r)^2.
since the new area is the same as the old area but increased by 53 cm^2, then A2 is equal to A1 + 53 cm^2.
You get two formulas:
A1 = pi * r^2
A1 + 53 = pi * (1.7 * r)^2
simplify the second equation to get:
A1 + 53 = pi * 1.7^2 * r^2 which then becomes:
A1 + 53 = pi * 2.89 * r^2
your two equations have now become:
A1 = pi * r^2
A1 + 53 = pi * r^2 * 2.89
Subtract the first equation from the second equation to get:
A1 + 53 - A1 = pi * r^2 * 2.89 - pi * r^2
simplify this to get:
53 = pi * r^2 * 1.89
divide both sides of this equation by 1.89 * pi to get:
53 / (1.89 * pi) = r^2
solve for r^2 to get r^2 = 8.926150247
solve for r to get r = 2.987666355
That's the length of the original radius.
Multiply this by 1.7 to get r = 5.079032803
That's the length of the scaled radius that is 1.7 times as large as the original radius.
Solve for the respective areas using the respective radii.
Original radius gets an area of 28.04232804 square cm.
Enlarged radius gets an area of 81.04232804 square cm.
The difference is 53.
this confirms the solution is correct.
The solution to the question is that the radius of the new solar cell is equal to 5.079032803 cm.
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