Question

Question 2: A circular picture is 8 inches in diameter. Part A What is the area of the picture in square inches? A. 4π square inches B. 8π square inches C. 16π square inches D. 32π square inches Part B A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches? A. 4π square inches B. 12π square inches C. 36π square inches D. 40π square inches

really important please answer correctly

Answer 1

Answers:
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Part A) The correct answer is: [C]: " 16
`\pi` square inches " .
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Part B) The correct answer is: [C]: " 36
`\pi` 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 =
`\pi * r^2` ;

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 =
`\pi` * (4 in)² =
`\pi` * 4² * (in)² ;

=
`\pi` * (4*4) * (in²) ;

=
`\pi` * 16 * in² ;
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→ which is: Answer choice: [C]: " 16
`\pi` 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 = 
`\pi` * r² ;

= 
`\pi` * (6 in)² ;

=
`\pi` * (6²) * (in²) ;

=
`\pi` * (6*6) * (in²) ;

=
`\pi` * (36) * (in²) ;
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 → which is: Answer choice: [C]: " 36
`\pi` square inches " .
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