Final answer:
To find the radius of the base of the cone, we can use the volume of water it can hold and the height of the cone. By applying the formula for the volume of a cone and solving for the radius, we find that the radius is approximately 2.26 meters.
Step-by-step explanation:
To find the radius of the cone's base, we can use the given information about the height and the volume of water it can hold. First, we convert the volume of water from liters to cubic meters by dividing by 1000. Then, we can use the formula for the volume of a cone, V = (1/3)πr^2h, where V is the volume, π is pi, r is the radius, and h is the height. Plugging in the values we have, we can solve for the radius of the base.
We know that the height of the cone is 24 m and it can hold 1232000 liters of water, which is equivalent to 1232 cubic meters. So, the volume of the cone is 1232 cubic meters. Using the formula for the volume of a cone, we can rewrite it as 1232 = (1/3)πr^2(24). Simplifying, we get r^2 = (3*1232)/(π*24) ≈ 16. Dividing both sides by π, we get r^2 ≈ 5.09. Finally, taking the square root of both sides, we find that the radius of the base of the cone is approximately 2.26 meters.
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