一條很簡單的數學問題

As the height of the solid is (2r＋3)cm, so the height of the right cylinder is (r＋3)cm.

(a) Total surface area is 216π cm^2, so
2πr(r＋3)＋πr^2＋(1/2)[4πr^2)＝216π
==> 5r^2＋6r－216＝0
==> (r－6)(5r＋36)＝0
==> r＝6 or -36/5 (reject)
Therefore, r＝6

(b) Total volume of the solid is :
(r＋3)πr^2＋(1/2)(4/3)πr^3
＝9(36π)＋(2/3)(216π)
＝342π＋144π
＝486π (cm^3)

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