1條Circular cylinder問題

Question

http://upload.lsforum.net/users/public/f12640Q18p132.gif

The figure shows a right circular cylinder with AC being a diameter of its upper face. AB and CD are two vertical lines on the curved surface. A curve is drawn as shown on the surface of the cylinder from B to C. If its shortest length is 6√(π^2 +1). Find the curved surface area of the cylinder.

Ans.: 24π cm^2

請問各位可詳細解釋中間的步驟嗎?
THZ!>,<

? · Accepted Answer

圖片參考：http://i1295.photobucket.com/albums/b635/ToineCheung/01_zps92ef9956.jpg
基本上你可以將它拆做一個三角形，斜邊正是那條曲線的長度，高是 6cm，底是1.5個圓周（因為圖內它圍了1.5個圈）       [6√(π² +1)]² = [(3/2)(2πr)]² + 6² (Pyth. Theorem)   36π² + 36 = 9π²r² + 36   36π² = 9π²r²   r = 2cm       The curved surface area   = πr²h   = π(4)(6)   = 24π cm²

1條Circular cylinder問題

1 個解答