A sector of a circle has a central angle of 30. Find the area of the sector if the radius of the circle is 7 cm.

Answer 1

A sector of 30º is (30/150) = 1/12 of the entire area of the circle.

The area of a circle is: A_C = ∏r²

^{The radius of the circle is 7 cm. That means that the diameter of the circle is 14 cm because d = 2r. I mention that because 7 cm. is what I call a "magic number" (a number that makes the calculations easy so you may concentrate on the problem). Here, you may use the very inexact estimate that ∏ = 22/7/}

^A_C = ^. ∏r² = ∏(d/2)² = ∏d²/4 = (22/7)(14)²/4 ≅ 154 cm²

Now,, if you use the better approximation of ∏ = 3.14:

A_C = (3.14)(7)² = cm²

Then, you find the area of the sector: A_S / A_C = α_S/α_C

A_S = A_{C *} α_S/α_C

A_S = ∏r² (30/360)

A_S = ∏7² (1/12)

A_S = (49/12)∏ (now, use an approximation for ∏)