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