Question

Please help picture shown and show workkkk

Answer 1

1)
Area of largest circle - 2 * Area of one smaller circle = Area of the shaded region

AE = diameter of large circle = 48cm
radius of larger circle = diameter / 2 = 48cm / 2 = 24cm

4 circles fit across the diameter of the circle, so the diameter of the larger circle = 4 * diameter of the smaller circle
diameter of larger circle = 48cm = 4 * diameter of the smaller circle
diameter of the smaller circle = 48cm / 4 = 12cm
radius of smaller circle = diameter / 2 = 12cm / 2 = 6cm

Area of a circle = pi * r^2

Now plug the circle area equation into the first equation:

`A_(shaded)=A_(l) - 2*A_(s)\\\\A_(shaded)=[\pi (r_(l))^(2)]-2*[\pi (r_(s))^(2)]\\\\A_(shaded)=[\pi (48cm)^(2)]-2*[\pi (6cm)^(2)]\\\\A_(shaded)=2304\pi-72\pi\\\\Area\ of\ shaded\ region\ is\ 2232\pi.`


2)
Area of the shaded region = 2/7 * Area of the smaller circle
Area of the unshaded region = Area of larger circle + Area of smaller circle - Area of shaded region * 2

`A_(unshaded)=[\pi (r_(1))^(2)]+[\pi (r_(2))^(2)]-2*[\pi (r_(2))^(2)]*(2)/(7)\\\\A_(unshaded)=[\pi (10cm)^(2)]+[\pi (7cm)^(2)] -(4)/(7)[\pi (7cm)^(2)]\\\\A_(unshaded)=100\pi\ cm^(2)+49\pi\ cm^(2)-(4*49\pi\ cm^(2))/(7)\\\\A_(unshaded)=149\pi\ cm^(2)-(4*7*\pi\ cm^(2))\\\\A_(unshaded)=149\pi\ cm^(2)-28\pi\ cm^(2)\\\\\\A_(unshaded)=121\pi\ cm^(2)`