KS3

How to show the volume of a cone is ⅓ height × πr²

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A short video showing how to prove the volume of a cone is ⅓h x πr².

How to prove the volume of a cone is ⅓ height × πr² slideshow

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WHAT YOU NEED: card, compass, scissors, sticky tape, a glass and a jug of water.
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STEP 1: Place a glass at the bottom left corner of the paper. Mark the centre point at the top of the glass.
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STEP 2: Set the compass radius so it’s equal to the distance between the mark and the bottom corner of the card.
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Keeping the compass at this width, draw a circle with it in the middle of the card. Use the scissors to cut out the circle.
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Use the ruler to draw a line from the centre of the circle to the edge of the circle, then use the scissors to cut along the line.
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Roll the circle into a cone, ensuring that the circumference of the cone is the same as the top of the glass. The heights are also the same.
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STEP 3: Seal the cone with sticky tape so its watertight. Then carefully fill the cone to the brim with water from a jug and pour the water into the empty glass.
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STEP 4: Fill the cone three times in total and empty into the glass. Three cones of water should fill the glass to the top. The glass is a cylinder with volume base x height. So the volume of a cone = 1/3 base x height.

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