Question

The weight of solid cylinder varies as the square of its diameter and its height jointly. A cylinder having 3 cm diameter and 5 cm height weighs 450 gms. What is the weight of a cylinder having 5 cm diameter and 6 cm height.

Answer 1

$$\begin{gathered} \mathrm{Let}W,d\mathrm{and}h\mathrm{denote}\mathrm{the}\mathrm{weight},\mathrm{diameter}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{cylinder},\mathrm{respectively}. \\ Weknowthat\mathrm{W}\mathrm{varies}with{d}^2\mathrm{and}h(takentogether). \\ \mathrm{We}\mathrm{have}: \\ W\alpha d^{2}h \\ \therefore W=k{d}^{2}h\left(k\mathrm{is}a\mathrm{constant}.\right) \\ Now, \\ W=450\mathrm{gm},d=3\mathrm{cm}\mathrm{and}h=5\mathrm{cm} \\ Thus,wehave: \\ 450=k\times {\left(3\right)}^2\times 5 \\ \Rightarrow k=\frac{450}{45} \\ \Rightarrow k=10 \\ E\mathrm{quation}\mathrm{of}\mathrm{variation}\mathrm{is}: \\ W=10d^{2}h \\ Here,d=5\mathrm{cm}\mathrm{and}h=6\mathrm{cm}. \\ Thus,wehave: \\ W=10\times {\left(5\right)}^2\times 6 \\ \Rightarrow W=1500\mathrm{gm} \end{gathered}$$