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)

Answer 1

so whats the answer

Answer 2

The formula for the volume of a cylinder is given by:

Volume = πr^2h

Since the radius of the cylinder is the same as the sphere's, and the height is equal to the sphere's diameter, we can replace r with the sphere's radius and h with twice the sphere's radius:

Volume = π(r^2)(2r)

The volume of the sphere is given to be 48 m^3. Since the volume is the same for both the sphere and the cylinder, we can equate the two:

48 = π(r^2)(2r)

Simplifying the equation, we get:

48 = 2πr^3

To find the volume of the cylinder, we need to solve for r:

r^3 = (48 / (2π))

r^3 = (24 / π)

r = (24 / π)^(1/3)

Substituting this value of r back into the equation for the volume of the cylinder, we get:

Volume = π((24 / π)^(2/3))(2(24 / π)^(1/3))

Simplifying, we can calculate the approximate value of the volume.

Answer 3

The exact volume of the cylinder cannot be determined without knowing the value of π. However, the approximate value of the volume can be calculated using a rough approximation for π.

Let's assume π is approximately equal to 3.14.

Plugging this approximation into the equation, we get:

Volume ≈ 3.14((24 / 3.14)^(2/3))(2(24 / 3.14)^(1/3))

Calculating these values, we find that the approximate volume of the cylinder is approximately 334.64 m^3.