Question

2what is the area of a circle to the nearest square inch when the circumference is 75.1 use 3.14

Answer 1

The correct answer is "452 in² " .

(assuming that the given value for the circumference is in "inches".

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Step-by-step explanation:
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Area, "A" of a circle:

A =
`\pi` * r² ;

in which "r = the radius" .

We are given the Circumference, "C" of the circle:
C = 75.1 = 2 *
`\pi` * r ;

Using "3.14" for
`\pi` ;

Let us find the value for "r" (the radius"; so we can plug that value into the formula to find the area of the circle.

C = 2 *
`\pi` * r ;

→ 75.1 = 2 * 3.14 * r ;

Solve for "r" ;

→ 2 * 3.14 * r = 75.1 ;

Divide each side of the equation by: "(3.14 * 2)" ; to isolate "r" on one side of the equation; & to solve for "r" ;

→ [2 * 3.14 * r] / [2 * 3.14] = 75.1 / [2 * 3.14] ;

→ r = 75.1 / [2 * 3.14] ;

= 75.1 / (6.28) ;

= 11.9585987261146497 ; round to "12" ;

→ r = 12 ;
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To solve for the area of the circle:

Area, "A" =
`\pi` * r² ;

We are told to use: "3.14" for
`\pi` ; and we can substitute our calculate value of "12" for "r" ;

→ A = (3.14) * 12² ;

= (3.14) * 144 ;

= 452.16 ; round to the nearest square inch; assuming that the given values are in inches; we round to:

→ "452 in² " .
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