Question

find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations)

Answer 1

Answer:

Step-by-step explanation:

the area of the hemisphere is  1/2 $\pi$$r^{2}$

the radius is 1/2 the diameter,

the diameter is also the hypotenuse of the isosceles triangle

$d^{2}$ = $4^{2}$+$4^{2}$

$d^{2}$ = 32

d =$\sqrt{32}$

r = 1/2$\sqrt{32}$

1/2$\pi$(1/2$\sqrt{32}$)^2

1/2$\pi$(1/4*32)

(32/8 )*$\pi$

4$\pi$ ( the entire upper hemisphere )

area of the triangle is  1/2* 4 *4 = 8

then the exact area of the parts of the circle would be

4$\pi$ - 8