4.6 I) Spheres – Part 1
The sphere below has a radius of 5 cm. What is the volume and the surface area of the sphere below? Give your answers to one decimal place.
Let’s work out the volume first.
The volume of the sphere is 523.6 cm3.
Now let’s find the surface area of the sphere and we do this by subbing in r as 5 in the formula below.
The surface area of the sphere is 314.2 cm2.
We are now going to have a look at a question that requires us to use one of the formulas to work backwards.
The exact surface area of a sphere is 196π cm2. What is the radius of the sphere and what is the volume of the sphere? Give the volume of the sphere to one decimal place.
The question gives us the surface area of the sphere. We are able to work out the radius of the sphere by setting the surface area of the sphere (196π) equal to the formula for the surface area of a sphere.
From looking at the above equation, we notice that both sides have a π in them. Therefore, the first step in finding the value of r is to divide both sides of the equation by π. By dividing both sides of the equation by π, we eliminate the π’s from both sides of the equation.
The next step is to divide both sides of the equation by 4.
We want to find the value of r and not r2. Therefore, we square root both sides of the equation.
The radius of the sphere is 7 cm. We are now able to work out the volume of the sphere by subbing the value for the radius into the volume of a sphere formula.
We now need to round the answer to one decimal place.
The volume of the sphere is 1436.8 cm3.