To find the length of the thread that the spider would create from the top-right back corner of the tank to the bottom-left front corner, we can use the three-dimensional distance formula. The tank's dimensions are given as follows:
- Length (width) = 35 inches
- Height = 16 inches
- Depth = 12 inches
We will define the coordinates of the points we are interested in.
-
Top-right back corner of the tank: This corner can be defined as (35, 0, 16) where:
- 35 is the length (x-coordinate),
- 0 is the depth (y-coordinate),
- 16 is the height (z-coordinate).
-
Bottom-left front corner of the tank: This corner can be defined as (0, 12, 0) where:
- 0 is the length (x-coordinate),
- 12 is the depth (y-coordinate),
- 0 is the height (z-coordinate).
Using the Distance Formula
The distance \( d \) between two points in three-dimensional space \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
Apply the Coordinates
Plugging in the coordinates from above:
- \( (x_1, y_1, z_1) = (35, 0, 16) \)
- \( (x_2, y_2, z_2) = (0, 12, 0) \)
The formula becomes:
\[ d = \sqrt{(0 - 35)^2 + (12 - 0)^2 + (0 - 16)^2} \] \[ = \sqrt{(-35)^2 + (12)^2 + (-16)^2} \] \[ = \sqrt{1225 + 144 + 256} \] \[ = \sqrt{1625} \]
Calculating the Square Root
Now we calculate \( \sqrt{1625} \):
\[ \sqrt{1625} \approx 40.31 \]
Rounding
Finally, rounding \( 40.31 \) to the nearest tenth gives us:
\[ \approx 40.3 \text{ inches} \]
Thus, the approximate length of the spider's thread would be 40.3 inches.