Problem solve

[almer]

1.A cylinder has a base whose radius is r. It is reduced in such a way that its radius is 1/2 r. If the initial volume of the cylinder is 480 cm3, find its volume after the reduction.

 

[Deleted member 4993]

1.A cylinder has a base whose radius is r. It is reduced in such a way that its radius is 1/2 r. If the initial volume of the cylinder is 480 cm3, find its volume after the reduction.

The volume of a cylinder is a function of 'r' and 'h'. The problem statement above does not define the status of 'h'. Hence it cannot be solved (as stated - without assumption/s.)

 

[lookagain]

The volume of a cylinder is a function of 'r' and 'h'.
The problem statement above does not define the status of 'h'. Hence it <U>cannot <BR></U>
be solved (as stated - without assumption/s.)

It doesn't need to define the status of h. All it is stating
is that the new radius is \(\displaystyle 1/2\) of the original radius.
It would have mentioned the height if there had been a change
in it, but because it did not, the height here is immaterial.
This is not an assumption. It would be trying to read too
much into the problem, for this particular question.


-----------------------------------------------

Original radius = r

\(\displaystyle V = \pi r^2h\)

-----------------------------------------------


New radius = \(\displaystyle \frac{1}{2}r\)


\(\displaystyle V = \pi(\frac{1}{2}r)^2h = \)


\(\displaystyle \frac{1}{4}\pi r^2h\)


------------------------------------------------


Then the new volume is


\(\displaystyle \frac{1}{4}(480 \ cm^3) = \)

\(\displaystyle 120 \ cm^3\)