Question

Puja has two ropes measuring 5 m and 6 m. She ties a goat at point A with the 5 m rope and ties another goat at point B with the 6 m rope. Find out the ratio of areas grazed at point A and point B. The goats can only move inside the field.

• A. 25:36
• B. 26:37
• C. 24:36
• D. 25:37

Answer 1

The correct option is A

25:36

The area grazed by both the goats will be circular in shape as they are moving at a constant distance from a fixed point.


Hence, the area grazed when a goat is tied at a point with a rope would be a circle with radius equal to the length of the rope.

Area of a circle = $\pi r^2$.

Hence, the required ratio = $\frac{AreaatA}{AreaatB}$

= $(\frac{\pi r_A}{\pi r_B}{)}^2$

=$(\frac{r_A}{r_B}{)}^2$

= $(\frac{5}{6}{)}^2$ = 25:36 .