Find the diameter of a sphere whose volume is 113.04 cubic centimetres. Take 𝜋 to be 3.14.
In this question, we’re told the volume of a sphere, and we need to look backwards to work out its diameter. The formula for calculating the volume of a sphere is four-thirds multiplied by 𝜋 multiplied by 𝑟 cubed, where 𝑟 is the radius of the sphere.
We can use this formula and the known volume to set up an equation, which we can then solve to calculate the radius of the sphere. We’re told to use 3.14 to approximate 𝜋, so we have the equation four-thirds multiplied by 3.14 multiplied by 𝑟 cubed equals 113.04. Now we need to solve this equation.
First, we multiply both sides of the equation by three as there’s currently a three in the denominator of the left-hand side. This gives four multiplied by 3.14 multiplied by 𝑟 cubed equals 339.12. Next, we want to divide both sides of the equation by both four and 3.14. This gives 𝑟 cubed is equal to 339.12 divided by four multiplied by 3.14. This simplifies to exactly 27.
In order to find 𝑟, we need to take the cubed root of both sides of the equation. So now we have 𝑟 is equal to the cube root of 27. You should recall that 27 is a cube number, and the cube root of 27 is three. So now we know that the radius of the sphere is three and the units for this will be centimetres.
Remember the question didn’t ask us to find the radius; it asked us to find the diameter, but the diameter is just twice the radius. So if the radius of the sphere is three centimetres, then the diameter is six centimetres.