一題應用題 請幫我檢查做法

很明顯當底面半徑=高=6時
容量是216π
肯定是答案有問題

JJ ( 大師 5 級 )說出一個做數學的基本原則:
每一個題目做完之後一定要檢驗解是否正確。
如果無法直接驗證解之正確性，一定要用不同的方法，
反覆檢驗解是否合理(例如不同的方法，
不同的想法是否會得到相同的答案等)。
因為有些問題之解答過程實在太複雜，太細微，因此縱然有錯，也非常不容易檢查出來。最有名的例子之一:ABEL 第一次提除五次方程式根是解之歷史。請參考WIKI:
http://en.wikipedia.org/wiki/Niels_Henrik_Abel

2013-05-09 22:38:05 補充：
我將有關之部分節錄於下:
Abel had also started work on his first achievement, the quintic equation in radicals. Abel initially thought he had found the solution to the quintic equation in radicals in 1821. Mathematicians had been looking for a solution on this problem for over 250 years.

2013-05-09 22:38:45 補充：
The two professors in Christiania, Søren Rasmussen and Christopher Hansteen, found no errors in Abel's formulas, and sent the work on to the leading mathematician in the Nordic countries, Professor Ferdinand Degen in Copenhagen.

2013-05-09 22:39:16 補充：
He also found no faults, but still doubted that the solution, which so many outstanding mathematicians had sought for so long, could now really have been found by an unknown student in far-off Christiania.

2013-05-09 22:39:57 補充：
..........(略)
Degen asked Abel to give a numerical example of his method and, while trying to provide an example, Abel discovered a mistake in his paper.[3]

為什麼盡信解答
我曾經參與參考書的編纂校定
就找出了一堆的錯
那些解答也是人寫的
難保不出錯

回歸正題
最簡單的驗證法
r = l = 6 會得到 "容量為54π" 嗎

有錯嗎?

如果答案有錯, 那大概是不需要算 "上蓋" 部分吧?
不過, r=3, l=6 的答案看起來很漂亮應該沒錯吧?

如果要說解答的完整性的話, 就是需要確定那是極
小點.