I finished a differential approximation problem but I'm not sure I plugged in the right values.
"A cubic box is to be constructed with a volume of 100cm^3. Find the differential approximation to the maximum percentage error in the length of an edge of the cube if the maximum allowable percentage error in the volume of the cube is 0.75%."
So I take this to mean that the change in volume would be 0.75, (100 * 0.0075), which means I can approximate the change in a side-length. I'll display my work below and the answer, please tell me if this is correct.
Let S be a function of Volume representing a side-length, then S(V) = V^(1/3) since volume of a cube is the side-length cubed. Then:
dS/dV = 1/3V^(-2/3)
dS = 1/3V^(-2/3) * dV
dS = 1/3(100)^(-2/3) * 0.75 approximately equals 0.0116039721
Should the actual change, dS, be 100^(1/3) - 99.25^(1/3) which equals, rounded to 10 decimals, 0.0116331035 or 100.75^(1/3) - 100^(1/3) which equals, rounded to 10 decimals, 0.0115750824?
"A cubic box is to be constructed with a volume of 100cm^3. Find the differential approximation to the maximum percentage error in the length of an edge of the cube if the maximum allowable percentage error in the volume of the cube is 0.75%."
So I take this to mean that the change in volume would be 0.75, (100 * 0.0075), which means I can approximate the change in a side-length. I'll display my work below and the answer, please tell me if this is correct.
Let S be a function of Volume representing a side-length, then S(V) = V^(1/3) since volume of a cube is the side-length cubed. Then:
dS/dV = 1/3V^(-2/3)
dS = 1/3V^(-2/3) * dV
dS = 1/3(100)^(-2/3) * 0.75 approximately equals 0.0116039721
Should the actual change, dS, be 100^(1/3) - 99.25^(1/3) which equals, rounded to 10 decimals, 0.0116331035 or 100.75^(1/3) - 100^(1/3) which equals, rounded to 10 decimals, 0.0115750824?