S.3 Math

1. What is the percentage change in the volume of a cuboid if its base area is increased by 20% and its height is decreased by 10% ?
Let the original volume be x
The new volume = x(1 + 20%)(1 – 10%)
= x(1.2)(0.9)
= 1.08x
The volume is increased by (1.08x – x)/1.08x * 100% = 8%
2. The sides of a triangle have lengths 3, 6 and n is an integer. Find all possible values of n.
For a triangle, the sum of two sides is greater than the other side, so
3 + 6 > n = 9 > n ... (1)
3 + n > 6 => n > 3 ... (2)
6 + n > 3 = > n > -3 (which is always true)
So combining (1) & (2), 9 > n > 3
n can be 4, 5, 6, 7 or 8