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 $\pi$.

AdminMod2
Sep 27, 2017

#1**+2 **

*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 * 7^{2} * 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 * radius^{2}) * (height)

= (pi * 14^{2}) * 14

= (pi * 196) * 14

= 2744pi

The volume is 2744pi cm^{3} .

hectictar
Sep 27, 2017

#1**+2 **

Best Answer

*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 * 7^{2} * 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 * radius^{2}) * (height)

= (pi * 14^{2}) * 14

= (pi * 196) * 14

= 2744pi

The volume is 2744pi cm^{3} .

hectictar
Sep 27, 2017