If each side of a cube is reduced by 20% the volume of the cube will be reduced by
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Answer:
Let the side of cube be 'a'. So, volume will be a
3
.
Increased side of the cube a' = a + 3. Hence the increased volume = a
3
+2457.
Increased volume of cube =
a
3
+2457=a
3
+27+9a(a+3)[(a+b)
3
=a
3
+b
3
+3aba+b)]
⟹2457=27+9a
2
+27a
⟹9a
2
+27a−2430=0
⟹a
2
+3a−270=0
⟹a
2
+18a−15a−270=0
⟹a(a+18)−15(a+18)=0
⟹a=15cm
If the side was decreased by 20%, then side
′
a
′
=12cm. The corresponding volume will be 12∗12∗12=1728 cu. cm
Decrease =15∗15∗15−12∗12∗12=3375−1728=1647 cu. cm
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