Question 616846
The keyys to solving this problem:<ul><li>The "pointed end" of the pizza slice will the the center of the circle. An angle whose vertex is at the center of a circle is called a central angle.</li><li>Once we know that the angle is a central angle we can use the fact that the ratio of the angle to the whole circle, {{{2pi}}} radians, is equal to the ratio of the angle's arc to the circumference of the whole circle.</li></ul>First let's write expressions for the numerator and denominator of each ratio:
The angle is unknown so let's call that x.
The radians for the whole circle is {{{2pi}}}.
The angle's arc is given to us: 4.2 inches.
The circumference of the whole circle is {{{2pi*r = 2pi*6 = 12pi}}}<br>
We can now write an equation we can solve:
{{{x/(2pi) = 4.2/(12pi)}}}
We can get x by itself by just multiplying each side by {{{2pi}}}:
{{{(x/(2pi))*2pi = (4.2/(12pi))*2pi}}}
which simplifies as follows:
{{{x = 4.2/6}}}
{{{x = 0.7}}}
So the angle is 0.7 radians.