Question

Please help with explanation

Answer 1

Answer:

B

Step-by-step explanation:

The formula for a area of the first semi circle is

$\frac{1}{2} \times \pi {r}^{2}$

where r is the radius

Since 4 is the diameter, 2 is the radius

plug it in

$\frac{1}{2} \times \pi {2}^{2}$

$\frac{1}{2} \times 4\pi$

$2\pi$

so the area of the first circle is 2

$2\pi$

now let find the second circle

Since the semi circle is twice the area of AB the diameter is 8 so the radius is 4.

Put it in the equation.

$\frac{1}{2} \times \pi {4}^{2}$

$\frac{1}{2} \times \pi \times 16$

$8\pi$

Now let find the third circle

Since it is twice the size of the second circle, the diameter is 16 and the radius is 8.

$\frac{1}{2} \times \pi {8}^{2}$

$\frac{1}{2} \times 64\pi$

$32\pi$

Now let add the area of the semi circle

$32\pi + 2\pi + 8\pi = 42\pi$