底面直径是8厘米的圆钢,将其截成两段同样的圆钢,两段表面积的和是565.2平方厘米.求原来圆钢的体积?

Answer 1

设圆钢高为2h.
565.2=2[2(π*64/4)+π*8*h]
565.2=2[32π+8πh]
565.2=16π[4+h]
h=565.2/16π-4
体积V=2[(π*64/4)h]
=32πh
=32π(565.2/16π-4)
=32π*565.2/16π-32π*4
=2*565.2-128π
=1130.4-401.9
=728.5cm³