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

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 =
`√(32)`

r = 1/2
`√(32)`

1/2
`\pi`(1/2
`√(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