for our first lab, emilia decides to measure the density of a potato. they notice that it is an unusual…

for our first lab, emilia decides to measure the density of a potato. they notice that it is an unusual shape and floats, so it is hard to calculate its volume. the potatos mass is measured to be 378.9 g. they then cut the potato into a cube and measure that sides of the cube have length 4.31 inches and its mass is 62.9 g. for a uniform density potato, the mass and volume are proportional. (useful conversions: 1 inch = 2.54 cm, 1 cm = 10^(-2) m, 1g = 10^(-3) kg) part 1 in si units, what is the uncut potatos mass? (rtol=0.05, atol=1e-08) m = part 2 in si units, what is the mass of the potato cube? (rtol=0.05, atol=1e-08) m = part 3 in si units, what is the volume of the potato cube after it has been cut? (rtol=0.05, atol=1e-08) v =

for our first lab, emilia decides to measure the density of a potato. they notice that it is an unusual shape and floats, so it is hard to calculate its volume. the potatos mass is measured to be 378.9 g. they then cut the potato into a cube and measure that sides of the cube have length 4.31 inches and its mass is 62.9 g. for a uniform density potato, the mass and volume are proportional. (useful conversions: 1 inch = 2.54 cm, 1 cm = 10^(-2) m, 1g = 10^(-3) kg) part 1 in si units, what is the uncut potatos mass? (rtol=0.05, atol=1e-08) m = part 2 in si units, what is the mass of the potato cube? (rtol=0.05, atol=1e-08) m = part 3 in si units, what is the volume of the potato cube after it has been cut? (rtol=0.05, atol=1e-08) v =

Answer

Explanation:

Step1: Convert length of cube side to SI units

The side - length of the cube $l = 4.31$ inches. Since $1$ inch$=2.54\times10^{- 2}$m, then $l = 4.31\times2.54\times10^{-2}$m$=4.31\times0.0254$m$ = 0.109474$m.

Step2: Calculate volume of cube for density - mass relationship

The volume of a cube $V_{cube}=l^{3}=(0.109474)^{3}$m$^{3}\approx0.00131$m$^{3}$. The density of the potato cube $\rho_{cube}=\frac{m_{cube}}{V_{cube}}$, where $m_{cube} = 62\times10^{-3}$kg and $V_{cube}\approx0.00131$m$^{3}$, so $\rho_{cube}=\frac{62\times10^{-3}}{0.00131}$kg/m$^{3}\approx47.33$kg/m$^{3}$.

Step3: Find mass of un - cut potato

The mass of the un - cut potato $m_{1}=378\times10^{-3}$kg.

Step4: Find mass of potato cube in SI units

The mass of the potato cube $m_{cube}=62\times10^{-3}$kg.

Step5: Calculate volume of cut - potato cube

We already found $V_{cube}=(0.109474)^{3}$m$^{3}\approx0.00131$m$^{3}$

Answer:

Part 1: $m = 378\times10^{-3}$kg Part 2: $m = 62\times10^{-3}$kg Part 3: $V=(0.109474)^{3}$m$^{3}\approx0.00131$m$^{3}$