01:34:47

The volumes of two spheres are 729 in3 and 27 in3.
What is the ratio of their radii, rounded to the nearest whole number?

since 729 = 9^3 and 27 = 3^3, their volumes are in the ratio of (9/3)^3, so their radii are in the ratio of 3/1.

To find the ratio of the radii of the two spheres, we can use the formula for the volume of a sphere:

V = (4/3)πr³

Given that the volume of the first sphere is 729 in³, we can substitute this value into the formula:

729 = (4/3)πr₁³

Solving for r₁:

r₁³ = (729 * 3) / (4π)
r₁ = cubed root of [(729 * 3) / (4π)]

Similarly, for the second sphere, we have:

27 = (4/3)πr₂³

Solving for r₂:

r₂³ = (27 * 3) / (4π)
r₂ = cubed root of [(27 * 3) / (4π)]

Now that we have the values of r₁ and r₂, we can calculate the ratio:

Ratio = r₁ / r₂

Let's calculate the ratio using these steps.