the edge of a cubical box can be measured with an allowable error of 2 mm. What is the corresponding error in the total surface area of the cubical box whose edge is one meter.

240cm^2

To determine the corresponding error in the total surface area of the cubical box, we can use the formula for the surface area of a cube, which is given by 6 times the square of the edge length.

Let's begin by finding the surface area of the cube with an edge length of 1 meter.

Surface area of a cube = 6 * (Edge length)^2

Given that the edge length is 1 meter, we can substitute this value into the formula:

Surface area of the cube = 6 * (1)^2
Surface area of the cube = 6 * 1
Surface area of the cube = 6 square meters

Now, let's determine the maximum and minimum possible edge lengths due to the allowable error of 2 mm.

Maximum edge length = 1 meter + 2 mm
Minimum edge length = 1 meter - 2 mm

Converting millimeters to meters, we have:

Maximum edge length = 1 meter + 0.002 meters
Minimum edge length = 1 meter - 0.002 meters

Maximum edge length = 1.002 meters
Minimum edge length = 0.998 meters

Now, let's calculate the corresponding maximum and minimum surface areas using these edge lengths.

Maximum surface area of the cube = 6 * (Maximum edge length)^2
= 6 * (1.002)^2 square meters

Minimum surface area of the cube = 6 * (Minimum edge length)^2
= 6 * (0.998)^2 square meters

To find the corresponding error in the total surface area, we subtract the minimum surface area from the maximum surface area:

Corresponding error in surface area = Maximum surface area - Minimum surface area
= 6 * (1.002)^2 - 6 * (0.998)^2 square meters

Calculating the values:

Maximum surface area = 6 * (1.002)^2 square meters
= 6 * 1.004008 square meters
= 6.024048 square meters (approx.)

Minimum surface area = 6 * (0.998)^2 square meters
= 6 * 0.996004 square meters
= 5.976024 square meters (approx.)

Corresponding error in surface area = Maximum surface area - Minimum surface area
= 6.024048 square meters - 5.976024 square meters
= 0.048024 square meters (approx.)

Therefore, the corresponding error in the total surface area of the cubical box is approximately 0.048024 square meters.

To find the corresponding error in the total surface area of the cubical box, we need to consider the effect of the allowable error on each of the six faces of the cube.

The surface area of each face of the cube is given by the formula A = side * side, where 'side' represents the length of one edge of the cube.

Given that the edge of the box can be measured with an allowable error of 2 mm, we can calculate the percentage error in the length of one edge as follows:

Percentage error = (allowable error / actual length) * 100

In this case, the allowable error is 2 mm, and the actual length of one edge is 1 meter, which is equivalent to 1000 mm.

Percentage error = (2 mm / 1000 mm) * 100 = 0.2%

Now, to find the corresponding error in the surface area of each face of the cube, we multiply the percentage error by the actual surface area of each face:

Error in surface area of each face = Percentage error * Surface area of each face

Surface area of each face = side * side = (1 m * 1000 mm) * (1 m * 1000 mm) = 1,000,000 mm²

Error in surface area of each face = 0.2% * 1,000,000 mm² = 2000 mm²

Since there are six faces to consider, the total error in the surface area of the cubical box is:

Total error in surface area = Error in surface area of each face * Number of faces

Total error in surface area = 2000 mm² * 6 = 12,000 mm²

Therefore, the corresponding error in the total surface area of the cubical box whose edge is one meter is 12,000 mm².