The radius of a sphere is the cube root of 708 centimetres. Find its volume in terms of 𝜋.
If we think about a sphere, it has a radius from the centre to any point on the outside. And the volume of a sphere is four-thirds times 𝜋 times the radius cubed. We’re told that the radius of our sphere is the cube root of 708. And so, to find the volume, we substitute the cube root of 708 in for the radius value. And we recognize that if we have the cube root of something and we cube it, we’re saying the cube root of 708 times itself three times. And that will just equal 708. And so, the volume will be four-thirds 𝜋 times 708.
We can multiply four-thirds by 708, which will be 944. And then, we won’t estimate because our problem told us to leave this volume in terms of 𝜋. And so, we say that the volume is 944 𝜋. We’re still missing some units. We know that the radius was a measure of centimetres, which means our units is centimetres cubed. Volume always has cube units.
And the volume of this sphere is 944𝜋 centimetres cubed.