Potato Density

For their first lab, Aliyah decides to measure the density of a potato. They notice that it’s an unusual shape and floats, so it’s hard to calculate its volume. The potato’s mass is measured to be 296 \(g\). They then cut the potato into a cube and measure that the sides of the cube have length 3 inches, and the potato’s mass is 113 \(g\). For a uniform density potato, the mass and volume are proportional.

(Useful conversions: 1 \(\textrm{inch}\) = 2.54 \(cm\), 1 \(cm\) = \(10^{-2}\) \(m\), 1 \(g\) = \(10^{-3}\) \(kg\)).

Part 1

In SI units what is the potato’s mass (\(m_p\))?

Answer Section

Please enter in a numeric value in \(kg\).

Part 2

In SI units what is the cube of potato’s mass (\(m\_{cp}\))?

Answer Section

Please enter in a numeric value in \(kg\).

Part 3

In SI units, what is the volume of the cube of potato after it has been cut?

Answer Section

Please enter in a numeric value in \(m^3\).

Part 4

In SI units, what is the volume of the original potato?

(Hint: use proportional reasoning!)

Answer Section

Please enter in a numeric value in \(m^3\).

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.