The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Use pi = 22/7.
Get the complete, step-by-step math solution for: "The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Use pi = 22/7.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Identify given values and properties of a clock
The length of the minute hand is the radius of the circle traced by its tip. So, r=14 cm. A minute hand completes one full revolution (360∘) in 60 minutes.
Step 2: Calculate the angle covered in 5 minutes
In 60 minutes, the minute hand covers an angle of 360∘. Therefore, in 5 minutes, the angle covered will be a fraction of 360∘. We calculate this as (5/60)×360∘=30∘.
Step 3: Calculate the area swept by the minute hand
The area swept by the minute hand is the area of a sector of a circle. The formula for the area of a sector is given by Area=360∘θ×πr2, where θ is the angle in degrees and r is the radius.
Step 4: Substitute values and calculate the area
Now, we substitute the calculated angle θ=30∘, the given radius r=14 cm, and π=722 into the area formula. This gives us 36030×722×(14)2.
Step 5: Simplify the expression to find the final area
First, simplify the fraction 36030 to 121. Then, calculate 142=196. Substitute these values: 121×722×196. We can cancel out 7 from 196, leaving 28. So, 121×22×28. Further simplification gives 31×22×7=3154. Dividing 154 by 3 gives approximately 51.33 cm2.