Question

a circular has a radius between 6.5cm and 7cm and a volume of 315cm. find the smallest height and the largest height of the cylinder with that volue. round to the nearest 100th

Answer 1

try radius of 6.5, then
πr^2h = 315
π(6.5)^2h = 315
h = 2.37

find the height for r = 7, then decide

just for fun, try a radius of 6.8 and see if it falls between your two values.

Answer 2

volume=h*PI*r^2

smallest height will be at 7cm
315/PI*7^2=2.05cm
largest height will be at 6.5cm
315/(PI* 6.5^2)=2.37cm

Answer 3

v = πr^2h, so h = v/(πr^2)
a larger r means a smaller h, so

315/(π*7^2) <= h <= 315/(π*6.5^2)
2.05 <= h <= 2.37