1, cut a cube for the first time, the volume is: 5 * 5 * 5 =125;

Cut a cube for the second time, the volume is: 4 * 4 * 4 = 64;

Cut a cube for the third time, the volume is: 2*2*2=8.

The remaining volume is: 5*6*9-( 125+64+8)=73.

2,3. 14*{60+(60+0. 15*2* 1)+(60+0. 15*2*2)+........+(60+0. 15*2*599)}

=1/2 * 3.14 * (239.6+60) * 600 = 282317.4 mm = 282.3 m (approximate value. )

3360 degrees.

4, x 2-3x+ 1 = 0, so:

x^2=3x- 1。

So x4+3x2+1= (x2) 2+3x2+1= (3x-1) 2+3 (3x-1)+1.

=9x^2-6x+ 1+9x-3+ 1=9x^2+3x- 1=9x^2+x^2= 10x^2，

So x2/(x4+3x2+1) = x2/10x2 =110.