设唱缸的棱长为x,则根据勾股定理可得:(\frac{x}{2})^2+(61\text{米})^2=x^2(\frac{x}{2})^2+(51\text{米})^2=x^2(\frac{x}{2})^2+(2\text{厘米})^2=x^2化简可得:x^2=4\times(61\text{米})^2+4\times(51\text{米})^2+4\times(2\text{厘米})^2x^2=148684\text{米}^2+10404\text{米}^2+16\text{米}^2x^2=159104\text{米}^2因此,唱缸的棱长为x=\sqrt{159104}\text{米}\approx398.86\text{米}。唱缸的棱长总和为4x=4\times398.86\text{米}=1595.44\text{米}。答:唱缸的棱长总和是1595.44米。