the minute hand of a clock is 10 cm long. through what exact distance does the tip move between 12p and 12:20 pm

circumference = 2 pi r = 20 pi cm

20min/60min = 1/3
so (1/3)20 pi = (20/3) pi cintimeters

To determine the distance covered by the tip of the minute hand between 12:00 PM and 12:20 PM, we need to calculate the angle swept by the minute hand and then use that angle to find the distance.

First, let's find the angle swept by the minute hand in 20 minutes (from 12:00 PM to 12:20 PM).

We know that a clock completes a full revolution of 360 degrees in 60 minutes. Therefore, for 20 minutes, the angle swept by the minute hand can be calculated as follows:

Angle swept = (Angle per minute) x (Number of minutes)
Angle swept = (360 degrees) ÷ (60 minutes) x (20 minutes)
Angle swept = 12 degrees per minute x 20 minutes
Angle swept = 240 degrees

Now, let's use this angle to find the distance covered by the tip of the minute hand.

The distance covered by the tip of the minute hand is equal to the circumference of a circle with a radius of 10 cm, multiplied by the fraction of the angle swept out of the full circle.

Circumference of a circle = 2 x π x radius

Since the radius is 10 cm, the circumference is:

Circumference = 2 x π x 10 cm
Circumference = 20π cm

To find the exact distance covered, we multiply this circumference by the fraction of the angle swept out of the full circle:

Distance covered = (Angle swept ÷ 360 degrees) x Circumference
Distance covered = (240 degrees ÷ 360 degrees) x (20π cm)
Distance covered = (2/3) x 20π cm
Distance covered = 40π/3 cm

Therefore, the exact distance covered by the tip of the minute hand between 12:00 PM and 12:20 PM is approximately 40π/3 cm.