Question

You have a small marble of Wolfgang Mozart. It is 10 inches tall and weighs 16 pounds. The original marble statue is 7 feet tall.

If the original statue were 20 feet tall, how much would it weigh?

Answer 1

Find the weight:

Since Solids are in similar shape

$\frac{\mathrm{Weight}\mathrm{of}\mathrm{small}\mathrm{marble}\mathrm{statue}}{\mathrm{Weight}\mathrm{of}\mathrm{original}\mathrm{marble}\mathrm{statue}}={\left(\frac{\mathrm{Height}\mathrm{of}\mathrm{small}\mathrm{marble}\mathrm{statue}}{\mathrm{Height}\mathrm{of}\mathrm{original}\mathrm{marble}\mathrm{statue}}\right)}^3$

$$\begin{gathered} \Rightarrow \frac{16}{\mathrm{W}}={\left(\frac{10}{140}\right)}^3 \\ \Rightarrow \frac{16}{\mathrm{W}}=\frac{1}{2744} \\ \Rightarrow 16\times 2744=\mathrm{W}\times 1 \\ \Rightarrow \mathrm{W}=439904 \end{gathered}$$

Hence, weight of the original statue is 43904 pounds