Video Transcript
Find the volume of a sphere whose
diameter is 4.2 centimeters. Use 𝜋 equal to 22 over seven.
Let’s begin by sketching the sphere
whose diameter is 4.2 centimeters. We know that the diameter of a
sphere is twice its radius. So, in our case, the radius is 4.2
divided by two. And that’s 2.1 centimeters.
Now recall that the volume 𝑉 of a
sphere is given by 𝑉 equals four over three 𝜋 times 𝑟 cubed, where 𝑟 is the
radius of the sphere. So, in our case, with a radius of
2.1 centimeters, we have the volume of the sphere equals four over three 𝜋 times
2.1 cubed. We’re told to use 𝜋 equal to 22
over seven. So we have four over three times 22
over seven times 2.1 cubed.
We can’t simplify this any further
since there are no common factors in the numerators and denominators. Hence, we evaluate this directly
using our calculator to find 𝑉 equals 38.808.
The volume of the sphere whose
diameter is 4.2 centimeters is therefore 38.808 cubic centimeters.
