If the length of the minute hand of the clock in London commonly known as "Big Ben" is 11.25' from the center of the clock to the tip of the hand, what is the area swept out by the minute hand as it moves 5 minutes of time?

Question

London

Mathematics

13 January, 14:26

If the length of the minute hand of the clock in London commonly known as "Big Ben" is 11.25' from the center of the clock to the tip of the hand, what is the area swept out by the minute hand as it moves 5 minutes of time?

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Brianna · Answer 1

A whole hour or revolution is 60 minutes and 360° so the area of a sector is:

A/πr^2=α/360

A=απr^2/360 ... now we need to find the angle α/360=5/60, α=30° so:

A=30πr^2/360

A=πr^2/12 and r=11.25ft so

A=11.25^2*π/12

A≈33.13 ft^2