a cube painted black is cut into 125 identical cubes .how many of them are not painted?
a. 21
b. 25
c. 27
d. 30
answer with steps please
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there are 6 faces in a cube
if u draw 5 lines at each faces and cut it along these lines then u will get 125 cubes
by analyzing method:
let there is a solid room made up of 125 bricks in cubical shape
and if u painted all walls and bottom with floor then it means u r painted 98 bricks over all so there will be 27 bricks will remain unpainted
if u draw 5 lines at each faces and cut it along these lines then u will get 125 cubes
by analyzing method:
let there is a solid room made up of 125 bricks in cubical shape
and if u painted all walls and bottom with floor then it means u r painted 98 bricks over all so there will be 27 bricks will remain unpainted
Shivayalaya:
i can sove it numerically if u want
s please
wait pls m in cls
ok but send
sure
can u send ques agin
numerically:
let edge of undivided cube = x unit
after dividing edge will be of small cube = x/5 unit
now remove x/5 unit length in each edge from each side then you will get cube with edge 3x/5 unit
volume of such cube = (3x/5)^3
while volume of small cube = (x/5)^3
as we know in such cube there is no painted face so total no. of unit cubes in it = (3x/5)^3/(x/5)^3
= 27
let edge of undivided cube = x unit
after dividing edge will be of small cube = x/5 unit
now remove x/5 unit length in each edge from each side then you will get cube with edge 3x/5 unit
volume of such cube = (3x/5)^3
while volume of small cube = (x/5)^3
as we know in such cube there is no painted face so total no. of unit cubes in it = (3x/5)^3/(x/5)^3
= 27
thanks
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