The volume of a sphere is 48m³ what is the volume of a cylinder if it's radius is the same ad the spheres and its height is equal to the spheres diameter

Answer 1

First, let's find the radius of the sphere since the cylinder's radius is the same. The formula to calculate the volume of a sphere is:

V = (4/3)πr³

To find the radius, we rearrange the equation:

r³ = (3V) / (4π)
r³ = (3 * 48m³) / (4π)
r³ = 144m³ / (4π)
r³ = 36m³ / π
r = (36m³ / π)^(1/3)
r ≈ 2.57m

Now, let's find the height of the cylinder since it is the same as the sphere's diameter. The diameter of a sphere is twice the radius:

d = 2r
d = 2 * 2.57m
d ≈ 5.14m

Since the height of the cylinder is equal to the sphere's diameter, the height of the cylinder is approximately 5.14m.

The formula to calculate the volume of a cylinder is:

V = πr²h

Substituting the values we found, we get:

V = π * (2.57m)² * 5.14m
V ≈ π * 6.6049m² * 5.14m
V ≈ 33.5173π m³

Therefore, the volume of the cylinder is approximately 33.5173π m³.