Which has the greater volume, a cube whose edges are four centimetres long or a cylinder with a radius of three centimetres and a height of eight centimetres?
To answer this question, we need to remember how to calculate the volume of both a cube and a cylinder. Let’s begin with the cube. A cube is a special type of rectangular prism or cuboid, in which all three of the cube’s dimensions are the same. We can refer to them as 𝑙.
The volume of a cube is therefore 𝑙 multiplied by 𝑙 multiplied by 𝑙, which we can write as 𝑙 cubed. We take the side length of the cube and then cube it. So the volume of the cube in this question, which has a side length or edge length of four centimetres, is four cubed. You may know what four cubed is equal to. But if not, we could first work out four squared, which is 16, and then multiply this by four. 16 multiplied by four is 64. So the volume of the cube is 64 centimetres cubed.
Next, let’s consider the cylinder. A cylinder is described by two measurements, its height ℎ and its base radius 𝑟. Its volume is given by 𝜋𝑟 squared ℎ. Here, 𝜋𝑟 squared gives the area of the circular base. And then, we multiply by eight, which is the depth of the prism. Our cylinder has a radius of three centimetres and a height of eight centimetres. So its volume is given by 𝜋 multiplied by three squared multiplied by eight. Three squared is equal to nine. And nine multiplied by eight is equal to 72. So the volume of the cylinder as a multiple of 𝜋 is 72𝜋.
Now, if we have a calculator, we can evaluate 72𝜋. And it gives 226.194 continuing. So we can see that the volume of the cylinder will be larger than the volume of the cube. But we can also see this if we don’t have a calculator. The number 𝜋 is approximately equal to 3.14. So 72𝜋 means 72 multiplied by something a little bit bigger than three. We can see that this is going to be bigger than 64 because 72 is already bigger than 64. And then, we’re multiplying it by three.
So we can conclude that the solid which has the larger volume is the cylinder.