Question

Determine the area of the circle given each measurement. The diameter is 8 in. Round the answer to the nearest hundredth.

Answer 1

Our answer is: A = 50.27 in².

`\Large\texttt{Explanation}`

We are asked to calculate the area of a circle, given that -

• the circle's diameter is 8 inches

The formula for a circle's area is as follows:

• 
  `\sf{A=\pi r^2}`

`\bigstar` Where -

• A = area
• r = radius (one-half of the diameter)

R A D I U S

• To find the radius, divide the diameter, d, by 2 -

8 ÷ 2 = 4 inches

Diagram of the circle:

`\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 4\ in}\end{picture}`

Substitute 4 for the radius -

`\sf{A=\pi*4^2}`

Square the radius -

`\sf{A=\pi*16}`

Multiply & round to 2 d.p. -

`\sf{A\approx50.27\:in^2}`

`\therefore` A = 50.27 in²

Answer 2

A ≈ 50.27 in²

Explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given diameter = 8 in, then r = 8 ÷ 2 = 4 cm , so

A = π × 4² = 16π ≈ 50.27 in² ( to the nearest hundredth )