Question

Please help me with the question

Answer 1

Answer: A 8
`\pi`

Explanation:

A=
`\pi r^(2)` so for larger
`16\pi =\pi r^(2)` and r=4 therefore d=8

To find the length of square I use the diameter of the larger circle as the diagonal of the square. Use pythagorean:

`d^(2) =x^(2)+ x^(2) \\8^(2) =2x^(2) \\64/2 = x^(2) \\x=√(32) =4√(2)` this is the length of the square side which is also the diameter of the inner circle

so the radius is x/2 r=2
`√(2)`

`A=\pi r^(2) =\pi (2√(2) )^(2) = \pi (2^(2) *2} )=8\pi`

Answer 2

Answer: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1

Step-by-step explanation: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1. In that case, the reason is very simple. The inner circle has an area of πr^2, and the outer circle has an area of π(2r)^2 = 4πr^2, where r is the radius of the inner circle.