Question

the area covered by hour hand of a wall clock between time 4.26 to 6.50 is what percent of the area covered by it in 15 hours​

Answer 1

Answer:

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius r=6. The circumference of that circle is

C=2πr=2π⋅6=12π.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is 1012π,

and the number of minutes that have expired since noon is 1012π⋅60≈16.

Therefore, to the nearest minute, the time is 12:16.

Hope it helps you!!!!!

Answer 2

Note: the question is incomplete as the area covered by the hour hand of the clock from 4.26 to 6.50 is missing hence exact value of the area cannot be determined.

Solution:

Know that the hour hand forms $\[{30^ \circ }\]$ in one hour,

Therefore,

Find the angle formed by the hour hand in 15 hour.

$\[30 \times 15 = {450^ \circ }\]$

Understand that in one circle only 12 hours are covered which form an angle of $\[{360^ \circ }\]$.

Find the area covered by the clock.

$\[\begin{array}{l} = \pi {r^2} - \left( {\frac{{150}}{{360}}} \right)\pi {r^2}\\ = \pi {r^2}\left( {1 - \frac{5}{{12}}} \right)\\ = \pi {r^2}\left( {\frac{{12 - 5}}{{12}}} \right)\\ = \left( {\frac{7}{{12}}} \right)\pi {r^2}\end{array}\]$

Hence the area covered by the clock is $\[\left( {\frac{7}{{12}}} \right)\pi {r^2}\]$.