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
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