Question

В.

In the figure above, O is the center of the circle and
AC and BD are diameters of the circle. The
measure of ZAOB is twice the measure of ZBOC,
and the radius of the circle is 3. What is the area of
the shaded region?

Answer 1

D).
`(3)/(2) \pi\: units^2`

Step-by-step explanation:

Let the
`m\angle BOC = x\degree`

`\therefore m\angle AOB = 2x\degree`

`\because m\angle AOB+m\angle BOC = 180\degree\\..(straight \: line \: \angle 's) \\</p><p>\therefore 2x + x = 180\degree \\</p><p>\therefore 3x = 180\degree \\\\</p><p>\therefore x = (180\degree)/(3)\\\\</p><p>\therefore x = 60\degree \\</p><p>\therefore 2x= 2* 60\degree = 120\degree \\</p><p>\implies m\angle BOC = 60\degree \\</p><p>\therefore central \: \angle \: (\theta) = 60\degree \\</p><p>Radius\: of \:circle \: (r) = 3\: units \\\\</p><p>Area \: of\: shaded \: region\\\\ = (\theta)/(360\degree)* \pi r^2 \\\\</p><p>= (60\degree)/(360\degree)* \pi * 3^2 \\\\</p><p>= (1 )/(6)* \pi * 9 \\\\</p><p>= (1 )/(2)* \pi * 3 \\\\</p><p>\huge \purple {\boxed {= (3)/(2) \pi\: units^2}} \\\\</p><p>`