Question

The number of angular points of a rectangular parallelepiped is x, number of edges is y and number of faces =z.Find the value of x-y+z?​

Answer 1

Answer:

2

Step-by-step explanation:

x = #vertices = 8    ( 4 at the bottom and 4 at the top )

y = #edges = 12     ( 4 at the bottom, 4 at the top, 4 vertical ones around the sides )

z = #faces = 6       ( top, bottom, left, right, front, back )

x - y + z = 8 - 12 + 6 = 2

Notice that what you're doing in this exercise is verifying Euler's Formula for this particular solid.  Do the same for other solids and you'll keep getting the same answer:  2.

e.g.

Tetrahedron:  x = 4, y = 6, z = 4, x - y + z = 4 - 6 + 4 = 2

Cube with a pyramid roof on it:  x = 9, y = 16, z = 9, x - y + z = 9 - 16 + 9 = 2

etc.

Answer 2

Answer:

2 is the answer

Step-by-step explanation:

x= 8(no. of angular points or vertices)

y= 12(no. of edges)

z= 6(no.of faces)

Therefore,

x-y+z

= 8-12+6

= -4+6

= 2.