The seconds hand on a watch is 14mm long. What area does it sweep through in 30 seconds?
What is the radius
What is yhe radius
Please solve this for me cause I don't know how to solve it
in 30 seconds it sweeps half of a circle
a = 1/2 π r^2
308
Abigeal
The second hand on a watch is 14mm long . what area does it sweep through in 30 seconds
I don't know how to solve it please solve it for me
To find the area swept by the seconds hand in 30 seconds, we can divide the motion of the seconds hand into 30 individual one-second intervals and calculate the area swept by each interval.
The seconds hand of a watch rotates about a fixed point, so we can consider each interval as a sector of a circle. The area of a sector can be calculated using the formula:
Area = (θ/360) * π * r^2
where θ is the central angle of the sector and r is the length of the seconds hand.
Since the seconds hand travels a full circle in 60 seconds, each one-second interval corresponds to a central angle of 360/60 = 6 degrees.
Substituting the values into the formula, we have:
Area = (6/360) * π * (14mm)^2
Calculating this expression, we can find the area swept by each one-second interval of the seconds hand.
Finally, to find the area swept by the seconds hand in 30 seconds, we multiply the result obtained by 30.
Solving this calculation will give us the area swept by the seconds hand in 30 seconds.