Answer:
- difference = 4πx +20π
- 214 square units
Step-by-step explanation:
Part A.
Do what the problem statement tells you, making the necessary substitutions.
Difference of areas = Circle B area - Circle A area
difference = π(x+6)² - π(x+4)² . . . . . . substitute for r in the circle formulas
= π(x² +12x +36) -π(x² +8x +16) . . . . . expand the squares
= π((x² -x²) +(12x -8x) +(36 -16)) . . . . . combine like terms
= π(4x +20) . . . . . . . . . . . . . . . . . . . . . this is the result of combining terms
difference = 4πx +20π . . . . . . . . . . . "simplified" form
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Part B.
For x=12, the above expression for the difference of areas becomes ...
difference = (3.14)(4·12 +20) = 3.14·68 ≈ 214 . . . . square units
