The number of times one needs to use the completely filled cone to completely fill the cylinder with water is <u>24</u>.
In the question, we are given that the radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
We are asked to find the number of times one needs to use the completely filled cone to completely fill the cylinder with water.
The volume of a cylinder is calculated using the formula, V = πr²h.
The volume of a cone is calculated using the formula, V = (1/3)πr²h.
In both the formulas r is the radius and h is the height.
The volume of the given cylinder using the formula is π(10)²(20) cm³ = 2000π cm³.
The volume of the given cone using the formula is (1/3)π(5)²(10) cm³ = (250/3)π cm².
The number of times one needs to use the completely filled cone to completely fill the cylinder with water =
The volume of the given cylinder/The volume of the given cone,
or, The number of times one needs to use the completely filled cone to completely fill the cylinder with water = {2000π cm³}/{(250/3)π cm²},
or, The number of times one needs to use the completely filled cone to completely fill the cylinder with water = 24.
Thus, the number of times one needs to use the completely filled cone to completely fill the cylinder with water is <u>24</u>.
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