Question

view this flea. What is the size of the flea? nt: use the % method to calculate the size.

Answer 1

The flea is present in a circle. Let the radius of the circle be R.

Hence the area of the circle will be $\pi R^2$

We can divide the circle into four sectors. The flea is present in the bottom right sector. This sector subtends an angle of 90degree at the center.

Hence the area of this sector will be given by the formula:

$Area = \frac{\theta}{360^{\circ}}\pi R^2$

where theta is the angle subtended at the center, Substituting the value gives:

$Area = \frac{90^{\circ}}{360^{\circ}}\pi R^2$

$\therefore Area = 0.25\pi R^2$

Therefore, the proportion of the figure occupied by the flea is:

$\frac{0.25\pi R^2}{\pi R^2} = 0.25 = 25\%$

Given the field of view which can be calculated based on the magnification, the 25% of that would be the size of the flea.