KS3

How to show a cone's surface area = π × r × slant length

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A short video showing how to prove the surface area of a cone is π × radius × slant length.

How to prove a cone's surface area slideshow

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Click to see a step-by-step slideshow.
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WHAT YOU NEED: piece of paper, ruler, compass, pencil, scissors.
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STEP 1: Use the compass to draw a circle and cut it out...
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…to create a cone, use the ruler to draw two lines outwards from the centre point of the circle - both at slight angles as above. Use the scissors to cut along the lines. Take the bottom part of the circle and roll it into a cone.
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STEP 2: Unroll it and fold the shape in half vertically. Use a ruler to draw along the fold, then shade half of the shape in using a pen.
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STEP 3: Cut the shape in half. Fold the two remaining shapes in half. Cut along the folds using scissors. You should be left with 4 identical sectors...
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…repeat. You should now be left with 8 identical sectors.
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STEP 4: Rearrange the sectors to form a rectangle...
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...the bottom edge of the rectangle is 1/2 of the circumference of the base of the cone. The height of the rectangle is the slant length...
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...you've done it! The sectors rearranged into the rectangle show the area of the curved surface of the cone = π × radius × slant length.

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