Answer:
C. [tex]33.13\text{ ft}^2[/tex]
Step by step explanation:
We have been given that 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.
Since a clock is in form of circle, so the length of minute hand will be radius of clock.
Since we know that 1 minute is equal to 6 degrees, so 5 minutes will be equal to 6*5=30 degrees.
Now we will use area of sector formula to find the area swept out by the minute hand as it moves 5 minutes of time.
[tex]\text{Area of sector}=\frac{\theta}{360}*\pi r^2[/tex], where,
[tex]\theta[/tex] = Central angle of sector,
r = radius of circle.
Upon substituting our given values in above formula we will get,
[tex]\text{Area of sector}=\frac{30}{360}*\pi*11.25^2[/tex]
[tex]\text{Area of sector}=\frac{1}{12}*3.14*11.25^2[/tex]
[tex]\text{Area of sector}=\frac{1}{12}*3.14*126.5625[/tex]
[tex]\text{Area of sector}=\frac{1}{12}*397.40625[/tex]
[tex]\text{Area of sector}=33.1171875\approx 33.12[/tex]
Therefore, the area swept out by the minute hand as it moves 5 minutes of time is 33.12 square feet and option C is the correct choice.
