Chapter 68, Problem 4A

To determine

The weight of the baseplate.

Answer to Problem 4A

The weight of the baseplate is 20.5912kg.

Explanation of Solution

Given Information:

  

ρ=7752 kg/cm³

Concept used:

  $\begin{array}{l}Width=density\times volume\\ Volumeofcylinder=\frac{\pi \times diamete{r}^2\times height}{4}\\ Volumeofcuboid=length\times breadth\times height\end{array}$

  $Weigthofthebase-plate=densityofthebase-plate\times volumeofthebase-plate$

  $Volumeofcylinderwith4.322cmdiameter=\frac{\pi \times {4.322}^2\times 2.200}{4}$

  $Volumeofcylinderswith4.322cmdiameter(V_3)=32.27617c{m}^3$

  $Volumeofcylinderwith9.308cmdiameter=\frac{\pi \times {9.308}^2\times 2.200}{4}$

  $Volumeofcylinderwith9.308cmdiameter(V_2)=149.70121c{m}^3$

  $Volumeofcuboid=length\times breadth\times height$

  $Volumeofcuboid=36.925\times 36.925\times 2.2$

  $Volumeofcuboid(V_1)=2999.60237c{m}^3$

  $Volumeofthebaseplate=V_1-V_2-6V_3$

  $Volumeofthebaseplate=2999.60237-149.70121-6\times 32.27617$

  $V=2656.244c{m}^3$

  $Weigthofthebase-plate=densityofthebase-plate\times volumeofthebase-plate$

  $W=7752\frac{kg}{m^3}\times 2656.244c{m}^3\times {10}^{-6}\frac{m^3}{c{m}^3}$

  $W=20.5912kg$

Conclusion:

The weight of the baseplate is 20.5912kg.