Final answer:
To find the diameter of the base of the cylinder, calculate the volume using the formula V = πr²h. Then, find the radius using the formula r = sqrt(V/(πh)). Finally, double the radius to find the diameter.
Step-by-step explanation:
To find the diameter of the base of the cylinder, we first need to calculate the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that the height of the cylinder is 14cm and the curve surface area is 88cm², we can calculate the volume by rearranging the formula: V = 88cm²/14cm = 6.29cm.
Now that we know the volume of the cylinder is 6.29cm³, we can find the radius using the formula V = πr²h. Rearranging the formula, r = sqrt(V/(πh)). Plugging in the values, we get r = sqrt(6.29cm³/(3.142*14cm)) = 0.75cm.
Finally, we can find the diameter by doubling the radius: diameter = 2 * radius = 2 * 0.75cm = 1.5cm.