The volume of a cylinder is given by the formula V = πr²h. Since the height is the same as the radius for these water bottles, the volume of one water bottle is V = πr³.

Given that there are 18 water bottles, the total volume of water is 18πr³.

The volume of a sphere is given by the formula V = 4/3πR³. Since the water fills half of the earthen pot, the volume of the pot is 2 * 18πr³ = 36πr³.

Setting these two equal to each other, we get 4/3πR³ = 36πr³.

Solving for R/r, we get R/r = (36 * 3/4)^(1/3) = 3.

So, the ratio of the radius of the cylinder to the radius of the pot is 1:3.

Question

The volume of a cylinder is given by the formula V = πr²h. Since the height is the same as the radius for these water bottles, the volume of one water bottle is V = πr³.

Given that there are 18 water bottles, the total volume of water is 18πr³.

The volume of a sphere is given by the formula V = 4/3πR³. Since the water fills half of the earthen pot, the volume of the pot is 2 * 18πr³ = 36πr³.

Setting these two equal to each other, we get 4/3πR³ = 36πr³.

Solving for R/r, we get R/r = (36 * 3/4)^(1/3) = 3.

So, the ratio of the radius of the cylinder to the radius of the pot is 1:3.

Knowee AI · Accepted Answer

The volume of a cylinder is given by the formula V = πr²h. Since the height is the same as the radius for these water bottles, the volume of one water bottle is V = πr³.

Given that there are 18 water bottles, the total volume of water is 18πr³.

The volume of a sphere is given by the formula V = 4/3πR³. Since the water fills half of the earthen pot, the volume of the pot is 2 * 18πr³ = 36πr³.

Setting these two equal to each other, we get 4/3πR³ = 36πr³.

Solving for R/r, we get R/r = (36 * 3/4)^(1/3) = 3.

So, the ratio of the radius of the cylinder to the radius of the pot is 1:3.

18 cylindrical water bottles with height same as that of the radius are emptied into a spherical earthen pot. The bottles fill half of the initially empty earthen pot. Find the ratio of the radius of the cylinder and that of the pot?Choices:- 2:12 1:3 1:4 1:5

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