three metal cubes of side 6cm 8cm and 10cm are melted and recast into a big cube.Find its total surface area.
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Let the length of each edge of the new cube be a cm. Then
a
3
=(6
3
+8
3
+10
3
)cm
3
⇒a
3
=1728⇒a=12
Volume of the new cube =a
3
=1728cm
3
Surface Area of the new cube =6a
2
=6×12
2
cm
2
=864cm
2
Diagonal of the new cube =
3
a=12
3
cm
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