If the dimensions of cuboid decrease
its volume decreases
by 10% each, then it's volume decreases
by________
Answers
Answer:
Let a be the length of the side of cube.
Then volume of cube =a
3
Suppose length of cube increased by 10% i.e. New Length L=a+
100
10a
And breadth is decreased by 10%. i.e. New breadth B=a−
100
10a
So, the given with side a becomes a cuboid with length L, breadth B and height H=a
We know that,
Volume of a cuboid =Length×Breadth×Height
=L×B×H
=(a+
100
10a
)(a−
100
10a
)a
=(a
2
−
(100)
2
100a
2
)a
=(a
2
−
100
a
2
)a
=
100
99a
3
<a
3
Now, difference between volumes of cube and cuboid =a
3
−
100
99a
3
=
100
a
3
Thus, the percentage change in volume =
a
3
100
a
3
×100=1%
Now, Total surface area of a cube =6a
2
Total surface area of cuboid =2(LB+BH+LH)
=2((a+
100
10a
)(a−
100
10a
)+(a−
100
10a
)a+(a+
100
10a
)a)
=2((a
2
−
100
a
2
+a
2
+a
2
))
=2(
100
299a
2
)
=5.98a
2
<6a
2
Thus, the surface area decreases.
And percentage decrease in total surface area =
6a
2
0.02
2
×100=0.33%