Question

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?

Answer 1

Answer:

33.15 square inches.

Step-by-step explanation:

Given:

Length of the minute hand is 11.25' from the center of the clock to the tip of the hand.

Question asked:

What is the area swept out by the minute hand as it moves 5 minutes of time?

Solution:

As length of the minute hand is '11.25' from the center of the clock to the tip of the hand means radius of the circle, r = 11.25 inches.

First of all we will find area of circle swept by the minutes hand,

$Area\ of\ circle=\pi r^{2}$

                        $=\frac{22}{7} \times11.25\times11.25\\\\ =\frac{2784.375}{7} \\ \\ =397.77\ square\ inches$

When minute hand moves 60 minutes, it makes one circle of area 397.77 square inches.

By using unitary method, we will calculate area swept by minute hand in 5 minutes:-

In 60 minutes, area swept = 397.77 square inches

In 1 minute, area swept = $\frac{397.77}{60}$

In 5 minutes, area swept = $\frac{397.77}{60}\times5=\frac{1988.85}{60} =33.15\ square\ inches$

Thus, the area swept out by the minute hand is 33.15 square inches when  it moves 5 minutes.