SAT: 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?

В. In the figure above, O is the center of the circle

Ответ:

mooreadrian41235

29.01.2022

SAT

D). $\frac{3}{2} \pi\: units^2$

Explanation:

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

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

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

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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?

Ответ:

Ответ:

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