A cylindrical with a volume of 576πm^3 is circumscribed about a sq. prism which has one side of the base that measures 8m. what is the altitude of the cylinder?

Question

jamesj · Answer

Draw a diagram of the cross-section and you'll see the radius of the circle must be
$$ r = 4 \sqrt{2} $$

anonymous · Answer

i can't imagine the illustration

jamesj · Answer

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The length of each side of the square is 8; the length of the radius then is the hypothenuse of a right-triangle, where the other two sides are 4 and 4.

anonymous · Answer

i rearrange the formula and i got this -  h = V ÷ (pi)r2.

jamesj · Answer

Yes, of course, as 
$$ V = \pi r^2 h $$

jamesj · Answer

V of the cylinder that is.

anonymous · Answer

so , my formula is right ?

anonymous · Answer

but i don't know how to get the radius of the circle.

jamesj · Answer

Yes, your formula is correct.

For radius r, look again carefully at the diagram I've drawn above.  r is the hypothenuse of a right-angled triangle, the other two sides being half of a side of the square.

anonymous · Answer

do i need to find the LSA of the cylinder? LSA=2pier^2

anonymous · Answer

h= v/πr^2  
h= 576/π(4√2)^2 = 5.73m ?? is that right?

jamesj · Answer

No, V = 576.pi

anonymous · Answer

oh. i forgot . so h= 576π/π(4√2)^2 = 18m??

jamesj · Answer

yes

anonymous · Answer

but i really don't get the formula for the radius