Question

The volume of a sphere is 48 m3. 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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the cylinder, we need to first find the radius and height of the sphere.

Given that the volume of the sphere is 48 m^3, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

Where V is the volume and r is the radius.

Rearranging the formula to solve for the radius, we have:

r^3 = (3/4π)V

Taking the cube root of both sides, we get:

r = 3√((3/4π)V) (Equation 1)

Next, we need to find the height of the cylinder, which is equal to the sphere's diameter. The diameter of the sphere is twice the radius, so the height of the cylinder is also twice the radius.

h = 2r

Now we can find the volume of the cylinder. The formula for the volume of a cylinder is:

V_cylinder = πr^2h

Substituting the values we found, we have:

V_cylinder = π(3√((3/4π)V))^2 * 2(3√((3/4π)V))

Simplifying further:

V_cylinder = 6π * ((3√((3/4π)V))^3)

V_cylinder = 6π * (3/4π)V

V_cylinder = 18V

So, the volume of the cylinder is 18 times the volume of the sphere, which is 18 * 48 m^3 = 864 m^3.

Therefore, the volume of the cylinder is 864 m^3.