Find the length of the are on a circle of radius r intercept

Find the length of the are on a circle of radius r intercepted by a central angle theta. Round to two decimal a. s = 32.20 inches b. s = 15.68 inches c. x = 10.25 inches d. s = 34.20 inches e. s = 30.20 inches Find the area of the sector of the circle with radius r and central angle theta. Round to two decimal places. a. A almostequalto 12.57 square inches b. A almostequalto 5.14 square inches c. A almostequalto 6.28 square inches d. A almostequalto 1.14 square inches e. A almostequalto 3.14 square inches

Solution

Solution:

3)

As we know;

The distance along the arc can be given as:

Arc Length = × r (when is in radians)

so, Arc Length = ( × /180) × r.

arc length in this case = (123× /180) × 15 inches

=> arc length = 32.185 inches (32.20 inches approx)

4)

As we know;

the area of a sector for angle can be given as:

A =  ½ r²

=> A =   ½ 4² (/8)

=> A =

=> A = 3.14 sq-inches