Let be the volume, radius, and height of the original cylinder, respectively.
The new cylinder has a volume 8.9% greater than its original volume, which means the new volume is . The radius was increased by 10%, so the new radius is . The height was decreased by , which means the new height is .
Recall that the volume of a cylinder with radius and height is
So for the new cylinder, the volume equation is
Now , so we can cancel those factors and solve for :
The wording "earns 8% interest each year" does not make it clear whether the savings account interest is compounded. (It usually is in real life, but not always in math problems.) The graphical solution shows both simple interest and interest compounded annually.
Simple interest: the balances will both be $2941.18 after 5.88 years.
Compound interest: the balances will both be $3111.06 after 5.74 years.