Please help with explanation

Question

asked Jun 28, 2022 186k views

1 Answer

JRsz · Answer 1 · 2022-07-04T07:46:31+0000

Answer:

B

Explanation:

The formula for a area of the first semi circle is

$(1)/(2) * \pi {r}^(2)$

where r is the radius

Since 4 is the diameter, 2 is the radius

plug it in

$(1)/(2) * \pi {2}^(2)$

$(1)/(2) * 4\pi$

$2\pi$

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.

$(1)/(2) * \pi {4}^(2)$

$(1)/(2) * \pi * 16$

$8\pi$

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.

$(1)/(2) * \pi {8}^(2)$

$(1)/(2) * 64\pi$

$32\pi$

Now let add the area of the semi circle

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