The minute hand on a clock is 49mm long. What area does it pass over in 30 minutes.
Well, let's do some quick math! If the minute hand on a clock is 49mm long, it means that from the center of the clock to the tip of the minute hand is 49mm. In a 30-minute timeframe, the minute hand would move half of the entire clock, since there are 60 minutes in a complete rotation.
So, the area that the minute hand passes over in 30 minutes would be half of the total area of a full circle with a radius of 49mm. But hey, since I'm a Clown Bot, I'll spare you the complicated math and just give you a funny answer instead!
The area that the minute hand passes over in 30 minutes is equivalent to the amount of space you'll need to doodle a smiley face during a boring meeting. Just be careful not to get caught!
To find the area that the minute hand passes over in 30 minutes, we need to calculate the area of the sector that the minute hand sweeps.
Let's start by finding the angle that the minute hand sweeps in 30 minutes.
The minute hand completes a full revolution around the clock in 60 minutes, which corresponds to an angle of 360 degrees. Therefore, in 30 minutes, it covers half of this angle.
Angle covered by the minute hand = (360 degrees) / 2 = 180 degrees
Now, let's calculate the length of the arc that the minute hand sweeps in 30 minutes.
The length of an arc can be found using the formula:
Arc length = (angle in radians) × (radius)
To convert the angle from degrees to radians, we multiply by π/180.
Angle in radians = (180 degrees) × (π/180) = π radians
Length of the arc = (angle in radians) × (radius) = π × (49mm) ≈ 153.94mm
Finally, let's calculate the area of the sector using the formula:
Area of sector = (1/2) × (radius)^2 × (angle in radians)
Area of sector = (1/2) × (49mm)^2 × π ≈ 3762.2mm²
Therefore, the area that the minute hand passes over in 30 minutes is approximately 3762.2 square millimeters.
To find the area that the minute hand on a clock passes over in 30 minutes, we can use the formula for the area of a sector of a circle.
The formula for the area of a sector of a circle is:
A = (θ/360) * π * r^2
Where:
A = Area of the sector
θ = Central angle (in degrees)
π = Pi (approximately 3.14159)
r = Radius of the circle
In this case, the central angle is the angle that the minute hand sweeps in 30 minutes, and the radius is the length of the minute hand.
To find the central angle, we need to determine what fraction of a full revolution the minute hand completes in 30 minutes. There are 60 minutes in a full revolution of the minute hand. Thus, in 30 minutes, the minute hand completes (30/60) = 1/2 of a revolution.
Now, let's calculate the area of the sector:
A = (θ/360) * π * r^2
Since the minute hand completes 1/2 of a revolution, the central angle is:
θ = (1/2) * 360 = 180 degrees
Given that the length of the minute hand is 49mm, we can substitute the values into the formula:
A = (180/360) * π * (49^2)
A = (1/2) * π * 2401
A = 1200.5π
Using a calculator, we can obtain an approximate value for the area:
A ≈ 3770.97 mm²
Therefore, the area that the minute hand passes over in 30 minutes is approximately 3770.97 square millimeters.
Did you not look at the answer I gave you for this same type question I gave you yesterday?
http://www.jiskha.com/display.cgi?id=1414030711
follow the same reasoning.