+167 Find the number of cubic centimeters in the volume of the cylinder formed by rotating a square with side length 14 centimeters about its vertical line of symmetry. Express your answer in terms of $\pi$.
+9466 *edit*
Sorry about this! I didn't pay good enough attention here...the question says to rotate about the square's vertical line of symmetry, which makes a cylinder with a radius of 7 cm. and a height of 14 cm. Thanks to Alan for bringing this to my attention!!
So... the volume = pi * 72 * 14 = pi * 49 * 14 = 686pi cubic cm
I'll leave the old answer below even though I think it is wrong.
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The rotation will form a cylinder with a radius of 14 cm and a height of 14 cm, like this....
volume of cylinder = (pi * radius2) * (height)
= (pi * 142) * 14
= (pi * 196) * 14
= 2744pi
The volume is 2744pi cm3 .
+9466 *edit*
Sorry about this! I didn't pay good enough attention here...the question says to rotate about the square's vertical line of symmetry, which makes a cylinder with a radius of 7 cm. and a height of 14 cm. Thanks to Alan for bringing this to my attention!!
So... the volume = pi * 72 * 14 = pi * 49 * 14 = 686pi cubic cm
I'll leave the old answer below even though I think it is wrong.
----------
The rotation will form a cylinder with a radius of 14 cm and a height of 14 cm, like this....
volume of cylinder = (pi * radius2) * (height)
= (pi * 142) * 14
= (pi * 196) * 14
= 2744pi
The volume is 2744pi cm3 .
