The volume of a sphere is 48m ^ 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)
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48m^3, we can rearrange the formula to solve for the radius:
48 = (4/3)πr^3
r^3 = (3/4)(48/π)
r^3 = 18
r = ∛18
r ≈ 2.620
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. So the height of the cylinder is h = 2r ≈ 2(2.620) ≈ 5.24
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Plugging in the values, we get:
V = π(2.620)^2(5.24)
V ≈ 54.049
Therefore, the volume of the cylinder is approximately 54.049m^3.
is the bot right
Apologies, but I made a mistake in my response.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48m^3, we can rearrange the formula to solve for the radius:
48 = (4/3)πr^3
r^3 = (3/4)(48/π)
r^3 = 36/π
r = ∛(36/π)
r ≈ 2.653
The height of the cylinder is equal to the sphere's diameter, which is twice the radius. So the height of the cylinder is h = 2r ≈ 2(2.653) ≈ 5.307
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Plugging in the values, we get:
V = π(2.653)^2(5.307)
V ≈ 88.774
Therefore, the corrected volume of the cylinder is approximately 88.774m^3.