He points a = (2,1,1), and b = (3,2,3) are opposite corners of a solid box whose sides are parallel with the coordinate planes. find the length of the shortest path on the surface of the box from a to b.

The shortest path can be found by drawing the net for the box, then drawing a straight line on the net between the two points. There are two choices: cross an edge of length 1, or cross an edge of length 2. The latter gives the shorter path, whose length is

... d = √(2² + (1+1)²) = 2√2 ≈ 2.828 units

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In the diagram, the shorter path is the dashed line. The dotted line path has length √10 ≈ 3.162 units.

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It appears that the general solution to this sort of problem is that you want to cross the longest edge of the cuboid.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )