Question

PLEASE HELP ASAP SOLVE WITH EXPLANATION 3

Answer 1

3.4 in²

Explanation:

Information we must know:

• The radius of the circle is 2 inches so the diameter would be 4!
• The diameter of the square is equal to one side of the square
• Area of circle = πr²
• Area of square = l²

1) Find the area of the circle

• π × 2² = 12.5663706144
• We won't round up or down until the last step to get a more accurate answer!

2) Find the area of the square around the circle

• 4² = 16

3) Subtract!

• 16 - 12.5663706144 = 3.4336293856
• 3.4 in²

Have a lovely day :)

Answer 2

3.4 in²

Explanation:

We can solve for the area of the blue portion of this figure by subtracting the area of the circle (the area that is NOT blue) from the area of the surrounding square.

First, we can solve for the area of the square using arithmetic.

In this problem, the side length is twice the radius (
`r`) of the circle (given as 2 in), since the circle is circumscribed inside the square, meaning that it touches the square at all 4 midpoints of its sides.

`\textrm{side length} = 2r`

`\textrm{side length} = 2(2 \, \textrm{in})`

`\textrm{side length} = 4 \, \textrm{in}`

Now we can solve for the area of the square using the formula:

`\textrm{Area}_\square = \textrm{side length}^2`

`\textrm{Area}_\square = (4 \, \textrm{in})^2`

`\textrm{Area}_\square = 16 \, \textrm{in}^2`

Next, we can solve for the area of the circle using the formula:

`\textrm{Area}_\circ = \pi r^2`

Remember that the radius of the circle was given as 2 in.

`\textrm{Area}_\circ = \pi (2 \, \textrm{in})^2`

`\textrm{Area}_\circ = 4\pi \, \textrm{in}^2`

Finally, we can solve for the area of the blue portion of the figure by subtracting the area of the circle from the area of the square.

`\textrm{Area}_{\textrm{blue}} = A_\square - A_\circ`

`\textrm{Area}_{\textrm{blue}} = 16 \, \textrm{in}^2 - 4\pi \, \textrm{in}^2`

If we plug this into a calculator, we approximately get:

3.4 in²