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The volume of a sphere is 72 m3.
What is the volume of a cone if its radius is the same as the sphere's and its height is equal to the sphere's diameter? (1 point)
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To find the volume of the cone, we need to use the formula:
Volume of a cone = (1/3) * π * r^2 * h
Given that the radius of the cone is the same as the sphere's, we can calculate it as:
r = (diameter of sphere) / 2
Since the height of the cone is equal to the sphere's diameter, we have:
h = (diameter of sphere)
Substituting these values into the formula, we get:
Volume of cone = (1/3) * π * (diameter of sphere / 2)^2 * (diameter of sphere)
Now, to find the diameter of the sphere, we can use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * r^3
Given that the volume of the sphere is 72 m^3, we can solve for the radius as follows:
72 = (4/3) * π * r^3
Dividing both sides by (4/3) * π, we get:
r^3 = 72 / ((4/3) * π)
Simplifying further:
r^3 = (72 * 3) / (4 * π)
r^3 = 54 / π
Taking the cubic root of both sides:
r = (54 / π)^(1/3)
Now we can substitute this value for the radius and the diameter of the sphere into the formula for the volume of the cone:
Volume of cone = (1/3) * π * [(54 / π)^(1/3) / 2)^2 * (54 / π)^(1/3)
Simplifying further:
Volume of cone = (1/3) * π * (54 / (2π))^[2/3] * (54 / π)^[1/3]
This calculation is difficult to perform without a calculator.