Exams

A sinkhole (in Karst topography) is a hole in the ground that forms when water dissolves surface rock. Often, this surface rock is limestone, which is easily eroded, or worn away, by the movement of water.

Formation of a Sinkhole: In a landscape where limestone sits underneath the soil, water from rainfall collects in cracks in the stone. These cracks are called joints. Slowly, as the limestone dissolves and is carried away, the joints widen until the ground above them becomes unstable and collapses. The collapse often happens very suddenly and without very much warning. Water collects in these collapsed sections, forming sinkholes.

Sinkholes also form when the roofs of caves collapse. Sinkholes are often funnel-shaped, with the wide end open at the surface and the narrow end at the bottom of the pool.Sinkholes vary from shallow holes about 1 meter (3 feet) deep, to pits more than 50 meters (165 feet) deep.

Let the side of the square be x. Then, its diagonal = 2x2=2x 

Radius of incircle = x2 

Radius of circum circle= 2×x2=x2 

Required ratio = πx24:πx22=14:12=1:2