Answers:
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Part A) The correct answer is: [C]: " 16 [tex] \pi [/tex] square inches " .
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Part B) The correct answer is: [C]: " 36 [tex] \pi [/tex] square inches " .
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Note:
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Part A)
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The formula for the area, "A", of a circle:
A = [tex] \pi * r^2 [/tex] ;
in which:
" A = area of the circle" ;
" r = radius of the circle" ;
Note: radius, "r" = d / 2 ; in which: "d" is the diameter of the circle ;
Given: " d = 8 in " ; " r = (8 in) / 2 = 4 in " ;
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A = [tex] \pi [/tex] * (4 in)² = [tex] \pi [/tex] * 4² * (in)² ;
= [tex] \pi [/tex] * (4*4) * (in²) ;
= [tex] \pi [/tex] * 16 * in² ;
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→ which is: Answer choice: [C]: " 16 [tex] \pi [/tex] square inches " .
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Part B)
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We now have a circular frame with a thickness of "2 inches"
surrounding the original circle. This adds "4 inches" to the diameter of that of the original circle in "Part A" —
{Note: "2 inches on one side of the circle" ; PLUS "2 inches on the other side of the circle" ; equals "4 inches".}.
The diameter, "d", of this "new circle" ;
= "8 inches (that of the previous circle)" , PLUS "4 inches" , equals "12 inches" .
→ d = 12 in. ;
The radius , "r" :
→ r = d/2 = 12 in / 2 = 6 in.
→ r = 6 in.
The area, "A" of a circle:
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A = [tex] \pi [/tex] * r² ;
= [tex] \pi [/tex] * (6 in)² ;
= [tex] \pi [/tex] * (6²) * (in²) ;
= [tex] \pi [/tex] * (6*6) * (in²) ;
= [tex] \pi [/tex] * (36) * (in²) ;
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→ which is: Answer choice: [C]: " 36 [tex] \pi [/tex] square inches " .
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