Question

PLSSS HELP ITS DUE TOMMROW I WILL GIVE U MORE POINTS WHEN I GET MORE PLSSS

Answer 1

`A_{\text{red}} = 1766.25 \text{ in}^2`

Explanation:

We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:

`r_1 = (1)/(4) \cdot 30 = 7.5\\`

`r_2 = (2)/(4) \cdot 30 = 15\\`

`r_3 = (3)/(4) \cdot 30 = 22.5\\`

`r_4 = 30`

We can now find the area of each red band by subtracting:

the area of the circle within the white band just inward of the red band

-- from --

the area of the circle within the red band.

Finding the area of the outer red band:

`A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})`

`A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)`

↓ substituting the radius values into the circle area formula (
`\pi r^2`)

`A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)`

↓ using 3.14 for
`\pi`

`A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)`

↓ evaluating the right side

`A_{\text{outer red}} = 2826 - 1589.625`

`A_{\text{outer red}} = 1236.375 \text{ in}^2`

Finding the area of the inner red band:

`A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})`

`A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)`

↓ substituting the radius values into the circle area formula (
`\pi r^2`)

`A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)`

↓ using 3.14 for π

`A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)`

↓ evaluating the right side

`A_{\text{inner red}} = 706.5 - 176.625`

`A_{\text{inner red}} = 529.875 \text{ in}^2`

Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.

`A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}`

`A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2`

`\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}`