A block of wood is in the shape of a rectangular prism with dimensions n+5 cm, n+8 cm, and n+14 cm. All faces of the block are painted, and then the block is cut into 1cm cubes using parallel cuts to each face. If exactly half of the cubes have no paint on them, find the total number of cubes.

Volume of wood block :

V = (n+5)(n+8)(n+14)

Number of cubes = Volume of wood block/ Volume of small cubes

Number of cubes, N = (n+5)(n+8)(n+14)    1)

Number of cubes with on sides painted is :

n = (n+5-2)(n+8-2)(n+14-2)

n = (n+3)(n+6)(n+12)

It is given that :

n = N/2

(n+3)(n+6)(n+12) = (n+5)(n+8)(n+14)/2

Solving above equation, we get :

n = 2

Putting value of n in equation 1, we get :

N = (2+5)(2+8)(2+14)

N = 7×10×16

N = 1120  cubes

Therefore, number of cubes are 1120.

Hence, this is the required solution.

this doesn't make sense lol

i can not answer the question due to the fact that you spelled "carton" as "cartoon", a cartoon is something you watch on tv, a carton is a box that holds things. and also you've been waiting for this question for a while so why don't you get off your lazy a** and try to figure it out for yourself for once!

step-by-step explanation:

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look above, and leave your comments down below, and don't for get a five stars and a and brainliest xd

sorry for the stars in the middle of words its because it wouldn't let me submit. xd