First you need to use the formula
2πhr=a
since you know everything except for the height you can solve for h
2πh3=10
divide by 2
3πh=5
divide by 3π
h=5/3π
h=.530
Now you have height and lateral area
so you can use the formula
πa²h=v
where a is the lateral surface area, h is the height and v is volume
This works out to be a volume of
1.746 units squared