Question

A horse is tied outside a room with a rope of length 10 m. It can graze on the rest of the field. How much area can it graze?

• A. $\text{90}\pi m^2$
• B. $\text{75}\pi m^2$
• C. $\text{81.25}\pi m^2$
• D. $\text{86.25}\pi m^2$

Answer 1

The correct option is D $\text{86.25}\pi m^2$


The horse can graze the areas shown:
The yellow three-fourth circle and the pink quarter circle

The radius of the yellow part is 10 m, i.e., equal to the length of the rope (because the room has a length of 15 m, which is greater than the length of the rope).

The radius of the pink part is 5 m, which is equal to the rope length that is more than the width of the room (because the width of the room is less than the rope length).

Area of the yellow circle
$=\frac{3}{4}\times \pi \text{(r}\times \text{r)}$

r = 10

$=\frac{3}{4}\times \pi \text{(10}\times \text{10)}$
$=\frac{3}{4}\times \pi \times 100$
$=\text{75}\pi m^2$

Area of the pink circle
$=\frac{1}{4}\times \pi \text{(r}\times \text{r)}$

r = 5

$=\frac{1}{4}\times \pi \text{(5}\times \text{5)}$
$=\frac{1}{4}\times \pi \text{25}$
$=\text{6.25}\pi m^2$

Total area = $\text{75}\pi \text{+}\text{6.25}\pi$
= $\text{81.25}\pi m^2$