Math Questioin Regarding a Clock

Question

Question 1: An analog clock has a diameter of 10 inches, and the reading on the clock is 8:00. Find the following:

Part 1: The exact measure of the smaller central angle between the hands in radians.

Part 2: The length of the larger arc between the hands. Round to two decimal places. Be sure to include units. Part 3: The area of the smaller sector between the hands. Round to two decimal places. Be sure to include units.

Answer 1

radius =10/2 - 5 inches

time = 8:00

angle between hour and minute hands =

8/12 x 2pi= 4pi/3 radians = about 4.19 radians = obtuse angle

acute angle = 4/12 x 2pi= 2pi/3 = about 2.1 radians

you want the acute angle

length of the larger arc = radians times radius

= 4pi/3 x 5 = 20pi/3 inches = about 20.94 inches

area of the entire circle = 25pi

smaller sector area = (2pi/3)/2pi x25pi =25pi/3 = about 26.18 in^2