The minute hand of a clock is 6cm long. How far does the tip travel between noon and 1:30pm
To determine how far the tip of the minute hand travels between noon and 1:30 PM, we need to calculate the arc length covered by the minute hand within this time period.
Step 1: Calculate the circumference of the clock face.
The circumference of a circle is given by the formula C = 2πr, where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle (which is half the length of the minute hand). In this case, the length of the minute hand is given as 6 cm, so the radius is 6/2 = 3 cm.
C = 2π(3) = 6π cm (circumference of the clock face)
Step 2: Calculate the fraction of the clock face covered by the time period between noon and 1:30 PM.
The time between noon and 1:30 PM corresponds to half of the clock's total circumference because it represents half of a full rotation around the clock face.
Fraction of the clock face = 1/2
Step 3: Calculate the distance the tip of the minute hand travels.
To find the distance traveled by the tip of the minute hand, multiply the fraction of the clock face covered by the full circumference of the clock.
Distance = Fraction of clock face * Circumference
= (1/2) * 6π
= 3π cm
The tip of the minute hand travels approximately 3π cm between noon and 1:30 PM.