Question

Guys, can you please help me write an expression for shaded circle and please expand and simplify for me, guys, please? :)

Answer 1

OUTER CIRCLE AREA

• π(r+7)²

Inner circle area

• πr²

Area of shaded one

• π(r+7)²-πr²
• π(r²+14r+49-r²)
• π(14r+49)
• 14πr+49π

Answer 2

`\sf Shaded \: Area=14 \pi r+49 \pi`

Explanation:

Area of a circle

`\sf A=\pi r^2 \quad \textsf{(where r is the radius)}`

To find the area of the shaded area, subtract the area of the unshaded circle from the larger circle.

Area of the larger circle

`\implies \sf A=\pi (r+7)^2`

Area of the smaller (unshaded) circle

`\implies \sf A=\pi r^2`

Therefore, the area of the shaded area is:

`\implies \sf A=\pi (r+7)^2-\pi r^2`

Expand and simplify the expression:

`\implies \sf A=\pi (r+7)^2-\pi r^2`

`\implies \sf A=\pi (r^2+14r+49)-\pi r^2`

`\implies \sf A=\pi r^2 +14 \pi r +49 \pi -\pi r^2`

`\implies \sf A=14 \pi r+49 \pi`