Question Video: Finding an Unknown in a Given Formula by Direct Substitution Using Cube Roots

Video Transcript

The volume 𝑉 of a sphere with radius length 𝑟 is given by 𝑉 equals four-thirds 𝜋 𝑟 cubed. Find the radius length of a sphere with a volume of 4.851 times 10 to the third centimetres cubed. Take 𝜋 to be equal to twenty-two sevenths.

So if this is our volume formula and we know the volume is equal to 4.851 times 10 to the third centimetres cubed, let’s plug that in for 𝑉. So we plug this in for 𝑉.

And now looking at the other side of the equation, we bring down four-thirds. And instead of 𝜋, we will use twenty-two sevenths and we will be solving for 𝑟 cubed. So let’s first multiply the fractions together to multiply the numerators and multiply the denominators and reduce if possible.

So four-thirds times twenty-two sevenths is equal to eighty-eight twenty-first. Now to divide by this fraction, we essentially flip and multiply. So again when dividing by this fraction, we will flip eighty-eight twenty-first to be twenty-first eighty-eight and we will multiply.

And since this is equal to 𝑟 cubed, we’re going to have to cube root both sides. So we can replace 4.851 times 10 to the third with 4851. We will move the decimal place three units to the right and we will multiply by 21 divided by 88. And then we will take the cube root. And that will give us 10.5 centimetres.