Question

A hollow cylinder is made of gold. The mass of the object is 702,24 kg and the volume enclosed by the outside surface of the cylinder is 49,28 x 10-3 m3. What Is the radius of the cylindrical cavity if the height is 20 cm? gold = 19000 kg/m3

Answer 1

Answer on Question #58063-Physics-Mechanics

A hollow cylinder is made of gold. The mass of the object is $m = 702.24 \, kg$ and the volume enclosed by the outside surface of the cylinder is $V_{outer} = 49.28 \cdot 10^{-3} \, m^3$. What is the radius of the cylindrical cavity if the height is $h = 20 \, cm = 0.2 \, m$? $\rho_{gold} = 19000 \frac{kg}{m^3}$

Solution

$$V_{outer} = \pi R^2 h$$

The outer radius is

$$R = \sqrt{\frac{49.28 \cdot 10^{-3}}{\pi \cdot 0.2}} = 0.28 \, m.$$

The volume of hollow cylinder is

$$V = \pi (R^2 - r^2) h = \frac{m}{\rho} = \frac{702.24}{19000} = 36.96 \cdot 10^{-3} \, m^3$$

The radius of the cylindrical cavity is

$$r = \sqrt{\frac{V_{outer} - V}{\pi \cdot h}} = \sqrt{\frac{49.28 \cdot 10^{-3} - 36.96 \cdot 10^{-3}}{\pi \cdot 0.2}} = 0.14 \, m = 14 \, cm.$$

Answer: $0.14 \, m = 14 \, cm$.

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