“Why do we need to know this?” How often do we get these questions in the classroom? Sometimes in order for students to see the value in mathematics you must take it away from them.
Take for example the formula for the volume of a cylinder, V = (pi)(r^2)(h)
If you take away the (h) within the equation you are left with the equation for the area of a circle. Thus, as we know, a cylinder is simply a bunch of circles stacked over top of one another. But, do your students know this?
Here’s an exercise,
1) Bring in a printable worksheet with numerous circles of equal size2) As your students to cut out each circle
3) Next, ask them to find the sum of all the areas of each circle they cut out
4) Next, ask them to stack all the circles and use a ruler to measure its height
5) Finally, ask them to find the volume of the cylinder using V = (pi)(r^2)(h)
7) Wasn’t it a lot faster?
Take for example the formula for the volume of a cylinder, V = (pi)(r^2)(h)
If you take away the (h) within the equation you are left with the equation for the area of a circle. Thus, as we know, a cylinder is simply a bunch of circles stacked over top of one another. But, do your students know this?
Here’s an exercise,
1) Bring in a printable worksheet with numerous circles of equal size3) Next, ask them to find the sum of all the areas of each circle they cut out
4) Next, ask them to stack all the circles and use a ruler to measure its height
5) Finally, ask them to find the volume of the cylinder using V = (pi)(r^2)(h)
6) Does it closely resemble the sum of areas they previously calculated?
7) Wasn’t it a lot faster?
This doesn't work unless each circle is 1 unit high, which, if you print them on paper, is pretty unlikely.
ReplyDeleteCertainly there would be a margin of error here. My thought behind the idea was to make the connection between the two formulas.
ReplyDeleteI think the author of this post is right. The given argument or relation always works because the circle is a planner shape and there is no need to think about its height (there is no height for two dimensional shapes). LSquared took it a little wrong, as this concept always work ( Volume of solids = area of the base x the height of solid).
ReplyDeleteThe is no concept of height (third dimension) in planner geometry, hence no question of unit height of a circle.
The formula to find the volume of a cylinder is driven from area of base circle multiplying to its height, the same way as the formula to find the volume of any cube or cuboid is derived by multiplying the area of the bottom face to the height of the solid.
Manjit
area of the circle
بالرياض شركة تركيب مكيفات سبليت بالرياض
ReplyDeleteشركة تنظيف مكيفات سبليت بالرياض شركة تنظيف مكيفات سبليت بالرياض
شراء مكيفات مستعمله بالرياض شراء مكيفات مستعمله بالرياض
فني تركيب مكيفات سبليت بالرياض فني تركيب مكيفات سبليت بالرياض
شركة غسيل مكيفات بالرياض شركة غسيل مكيفات بالرياض
شراء مكيفات مستعمله بالرياض شراء مكيفات مستعمله بالرياض