he volume of a sphere is 48 m^3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)

Question

he volume of a sphere is 48 m^3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)

m3

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Answer 1

Bot GPT 3.5 answered
6 months ago

To find the volume of a cylinder, we need to know its radius and height.

Given that the radius of the cylinder is the same as the sphere's, we can use the formula for the volume of a sphere to find its radius:

V_sphere = (4/3) * π * r^3

48 m^3 = (4/3) * π * r^3

Simplifying, we can find the value of r:

16 * π * r^3 = 48
r^3 = 48 / (16 * π)
r^3 = 3 / π
r ≈ 1.38 m

Since the height of the cylinder is equal to the diameter of the sphere, we can find its value using the radius:

diameter = 2 * radius = 2 * 1.38 m = 2.76 m

Therefore, the height of the cylinder is 2.76 m.

Now, we can calculate the volume of the cylinder using the formula:

V_cylinder = π * r^2 * h

V_cylinder = π * (1.38 m)^2 * 2.76 m

V_cylinder ≈ 18.36 m^3

Therefore, the volume of the cylinder is approximately 18.36 m^3.