I have 2 things to say about this
1.
The radius of the big circle is twice the radius of the small circle and a circle is π(r^2), therefor 48π is equal to big circle minus small circle or (π(2r^2))-(π(r^2))
You can move the 2 in the first circle out of the parentheses by squaring it so you get
(4π(r^2))-(π(r^2). You’ll notice the equation is the same on both sides of the - except the left side is multiplied by 4 so you can subtract (1π(r^2) from (4π(r^2) to get
(3π(r^2))
Which means 48π=(3π(r^2))
Which simplies down, take the pi out as it’s top layer in both sides, divide 48 by 3 and it leaves you with
16=r^2 or r = 4
2. Technically that’s a bad test question because that’s not actually a circle, it’s an oval and it probably intends you assume it’s a circle. Turn the image sideways and it becomes more obvious
1.
The radius of the big circle is twice the radius of the small circle and a circle is π(r^2), therefor 48π is equal to big circle minus small circle or (π(2r^2))-(π(r^2))
You can move the 2 in the first circle out of the parentheses by squaring it so you get
(4π(r^2))-(π(r^2). You’ll notice the equation is the same on both sides of the - except the left side is multiplied by 4 so you can subtract (1π(r^2) from (4π(r^2) to get
(3π(r^2))
Which means 48π=(3π(r^2))
Which simplies down, take the pi out as it’s top layer in both sides, divide 48 by 3 and it leaves you with
16=r^2 or r = 4
2. Technically that’s a bad test question because that’s not actually a circle, it’s an oval and it probably intends you assume it’s a circle. Turn the image sideways and it becomes more obvious