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TSI Math: Comparing Volumes for Cylinders and Cubes 18 Views
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Description:
A cylindrical can of paint fits snugly on all sides inside a box. What is the ratio of the cylinder's volume to the box's volume?
Transcript
- 00:03
Okay sy mash members More modeling here A cylindrical can
- 00:07
of paint fits snugly on all sides inside a box
- 00:11
What's the ratio of the cylinders Volume to the boxes
- 00:15
Volume Say the cylinder has a radius of are in
- 00:19
the height of age the volume of the cylinder Then
Full Transcript
- 00:22
according to formulas pi r squared age right that's just
- 00:24
the formula You have to know it since a cylinder
- 00:26
fits snugly against the box on all sides will the
- 00:29
box has the same width and height There's a cylinder
- 00:31
just a different area formula the boxes based then measures
- 00:34
to our across each way So it looked like that
- 00:37
to our is the diameter of the cylinders Well the
- 00:40
boxes h units tall Well the volume of the box
- 00:43
is to our times to our times a door for
- 00:45
r squared h now take the ratio of the two
- 00:48
volumes That ratio is just another word for a fraction
- 00:51
so make a fraction out of the volumes We've got
- 00:52
the volume of the cylinder over the volume of the
- 00:54
box just fire squared H over four r squared age
- 00:58
well r squared in h cancel out leaving us with
- 01:01
a ratio of pi over four that's it The answer 00:01:04.56 --> [endTime] is a were shmoop
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