Question

Puja has two ropes measuring 5m and 6m. She ties a goat at point A with the 5m rope and ties another goat at point B with the 6m rope. Find the ratio of area that can be grazed by the goats at points A and 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, therefore:

Area of circle = $\pi r^2$

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.

Ratio = $\frac{AreaatA}{AreaatB}$ = $\frac{\pi r_A^2}{\pi r_B^2}$$(\frac{r_A}{r_B}{)}^2$ = $(\frac{5}{6}{)}^2$ = 25:36