the allowable error in the measurement of the edge of a cubical box is one mm. What is the corresponding error in the volume of a cubical box whose edge is 90 cm
To find the corresponding error in the volume of a cubical box, we need to calculate the derivative of the volume with respect to the edge length and then multiply it by the given allowable error.
The volume of a cube is given by the formula V = s^3, where s is the length of one side, or edge, of the cube.
In this case, the edge length of the cube is 90 cm. We need to convert it to meters since the allowable error is given in millimeters.
1 cm = 0.01 m
90 cm = 90 * 0.01 m = 0.9 m
Now we can find the derivative of the volume with respect to the edge length:
dV/ds = 3s^2
Substituting the edge length, we get:
dV/ds = 3(0.9)^2 = 2.43 m^2
Now we can multiply the derivative by the allowable error of 1 mm (0.001 m):
corresponding error in volume = 2.43 m^2 * 0.001 m = 0.00243 m^3
Therefore, the corresponding error in the volume of the cubical box is 0.00243 cubic meters.