Question

The volume of a sphere is 48 m³. What is the volume of a cylinder if it's radius is the same as the sphere's and its height is equal to the spheres diameter?

Answer 1

You HAVE to remember that the VOLUME of a Sphere is 2/3 the volume of a cylinder. BOT is wrong!

Answer 2

Let's first find the radius of the sphere. We can use the formula for the volume of a sphere:
V_sphere = (4/3) * π * r^3
We know that V_sphere = 48 m³. Therefore, we can rewrite the equation as:
48 = (4/3) * π * r^3
Dividing both sides by (4/3) * π gives us:
r^3 = 48 * 3 / (4 * π)
Simplifying further, we have:
r^3 = 36 / π
Taking the cube root of both sides, we find:
r ≈ 2.75 m

Now, let's find the height of the cylinder, which is equal to the sphere's diameter. Since the radius of the sphere is 2.75 m, the diameter is twice that or 2 * 2.75 = 5.5 m.

The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h
We substitute the values we have:
V_cylinder = π * (2.75)^2 * 5.5
Calculating this, we find:
V_cylinder ≈ 159.22 m³

Therefore, the volume of the cylinder with the same radius as the sphere and a height equal to the sphere's diameter is approximately 159.22 m³.