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Standard IX
Mathematics
Lateral surface area of a cube
Three cubes w...
Question
Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.
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Solution
Sum of volume of all the cubes melted will be equal to the volume of the new cube formed.
Let x be the edge of the new cube.
Hence,
x
3
=
3
3
+
4
3
+
5
3
=
27
+
64
+
125
=
216
=
6
3
⇒
x
=
6
c
m
Now, surface area of the new cube
=
6
×
(
e
d
g
e
)
2
=
6
×
6
2
=
216
c
m
2
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