3 cubes of a metal whose edges are in ratio 3:4:5are metal and converted into a single cube whose diagonal is 13 root of 3cm . find the edges of 3 cubes.
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1
Answer:
the edge of three cube 3x, 4x & 5x respectively.
volume of 3x cube =(3x)
3
=27x
3
4x cube =(4x)
3
=64x
3
5x cube =(5x)
3
=125x
3
total volume of three cubes =27x
3
+64x
3
+125x
3
=216x
3
volume of new cube = volume of three cubes
∴ a
3
=216x
3
∴ a=6x
→ diagonal of new cube =12
3
∴
a
2
+a
2
+a
2
=12
3
∴
3a
2
=12
3
∴
3
a=12
3
∴ a=
3
12
3
∴ a=12
→ a=6x
∴ 12=6x
x=2
The edge of three cubes 3×2 : 4×2 : 5×2
6 : 8 : 10
3x=3×2=6 cm
4x=4×2=8 cm
5x=5×2=10 cm
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