某兴趣小组要测量一金属块的密度,设计了如下方案:将装有适量细沙的薄壁圆筒,缓慢竖直放入盛有适量水的、水平放置的长方体透明薄壁容器中,待圆筒静止后,在圆筒上对应水面的位置标记一点A,并在长方体容器上标出此时的水位线MN(如图甲所示),此时水面距容器底部10cm;然后将待测金属块用细线悬挂在圆筒下方,缓慢竖直放入水中,圆筒静止后(金属块不接触容器底部),在长方体容器上标出此时的水位线PQ(如图乙所示);再向长方体容器中缓慢注水至圆筒上的A点与MN在同一水平面上(如图丙所示),测出PQ与此时水面的距离为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Eh%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1.3%3C%2Fmn%3E%3Cmtext%3Ecm%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 与MN的距离为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Eh%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.7%3C%2Fmn%3E%3Cmtext%3Ecm%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。若圆筒的底面积为100cm
2 , 长方体容器的底面积为400cm
2 , A点到圆筒底部的竖直距离h为4cm,水的密度为
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E1.0%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Ekg%2Fm%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmtext%3E3%3C%2Fmtext%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 不计细线的质量和体积。(g取10N/kg)
![](http://tikupic.21cnjy.com/ct20241o/ee/c1/eec10ee5e8923d1f16e84cc0cfcf36f0.png)