A cylinder has the curved surface
area of 656 centimetres squared and a diameter of 10.2 centimetres. Find its volume giving your answer
to the nearest cubic centimetre.
We’re given two pieces of
information about this cylinder. We’re told it has a diameter of
10.2 centimetres. We’re also told that its curved
surface area is equal to 656 centimetres squared. Our task is to find the volume of
the cylinder. So first let’s recall the formula
for calculating the volume. It’s 𝜋 𝑟 squared ℎ, where 𝑟 is
the radius of the cylinder and ℎ is the height.
We haven’t been given either of
these values directly within the question, so we need to use the information we have
in order to calculate them. Let’s start with the radius. The radius is always half of the
diameter, so if the diameter of the cylinder is 10.2, then the radius is 5.1.
The height is going to be a little
bit more complicated to work out, and we need to use the fact that we know — the
curved surface area. The curved surface area of a
cylinder is found using the formula two 𝜋𝑟ℎ or 𝜋𝑑ℎ. As we know the curved surface area
and we know the diameter, we can use these to form an equation that we’ll be able to
solve in order to find the height.
So substituting 10.2 for 𝑑 and 656
for the curved surface area, we have 𝜋 multiplied by 10.2 multiplied by ℎ is equal
to 656. Now, we could solve this equation
completely in order to find the height of the cylinder, but remember we’re then
going to substitute it into the formula for the volume. And the volume has a factor of 𝜋
ℎ. So instead of solving for ℎ
completely, let’s just so for 𝜋ℎ.
In order to do this, we need to
divide both sides of the equation by 10.2. We have that 𝜋ℎ is equal to 656
over 10.2. And we won’t evaluate there any
further as we’re now going to use it in our calculation of the volume. So now, we substitute the values of
𝜋ℎ and 𝑟 squared into the formula for the volume. We have the volume is equal to 656
over 10.2 multiplied by 5.1 squared. This gives a value of 1672.8
Finally, recall that the question
asked us to give the answer to the nearest cubic centimetre. So we need to round this value. Therefore, the volume of this
cylinder to the nearest cubic centimetre is 1673 cubic centimetres.