Subtract 336 from 432 to get the sum of two circular faces of a cylinder, then subtract 336 from the sum of the two circular faces to calculate the area of the remaining circle after the cylinder is removed, divide the sum of the two faces by two to get the area of one face, bring this area into the formula for calculating the circular area to get the circumference of the circle, and then divide the circumference by the area after the two circular faces are removed to get the height of the cylinder.

2:

Find the root of 39270 directly with the cubic to get an intermediate value (because it is a natural number, the decimal point should be rounded off), and then use this value to subtract 1 from the former and add 1 to get three consecutive natural numbers, and then bring these three numbers into the volume calculation formula to calculate whether the result is equal to 39270, and if it is correct, bring them into the surface area calculation formula. There may be errors in this method, but usually the number obtained after finding the root will be the intermediate number. If the conclusion is wrong, it can be regarded as the continuous calculation of the first number or the third number, which is faster.

The second method is about the decomposition of prime factors, which is more complicated.

I haven't touched these things for a long time, so I'm not clear about the decomposition prime factor, mainly because I'm too lazy to calculate it.

Then the number you get by finding the root of 39270 should be about 34, so the three natural numbers should be 33 34 35, so the length should be 33, the width should be 34 and the height should be 35.

Bring in the surface area formula 33*34*2+33*35*2+34*35*2 to get the result.

I haven't touched these things for a long time, and the expression may not be clear.