A rectangular box has dimensions x, y and z units, where x < y < z. If

1.	A rectangular box has dimensions x, y and z units, where x < y < z. If one dimension is only increased by one unit, then the increase in volume is (a) Greatest when x is increased (b) Greatest when y is increased (c) Greatest when z is increased (d) The same regardless of which dimension is increased.
Answer» (a) Greatest when x is increased We can check by an example. Let x = 2, y = 3, z = 4. Then Volume of box = 2 × 3 × 4 = 24 cu. units. If we increase x by 1 unit, keeping the other same i.e, x = 3, then new volume = 3 × 3 × 4 = 36 cu. units. If we increase y by 1 unit keeping the others same, i.e., y = 4, then new volume = 2 × 4 × 4 = 32 cu. units If we increase z by 1 unit keeping the other same, i.e., z = 5, then new volume = 2 × 3 × 5 = 30 cu. units. Hence the increase in volume is greatest, when x increases. You can check with other values also.

A rectangular box has dimensions x, y and z units, where x < y < z. If one dimension is only increased by one unit, then the increase in volume is (a) Greatest when x is increased (b) Greatest when y is increased (c) Greatest when z is increased (d) The same regardless of which dimension is increased.

Answer»

(a) Greatest when x is increased

We can check by an example. Let x = 2, y = 3, z = 4. Then

Volume of box = 2 × 3 × 4 = 24 cu. units.

If we increase x by 1 unit, keeping the other same i.e,

x = 3, then new volume = 3 × 3 × 4 = 36 cu. units.

If we increase y by 1 unit keeping the others same, i.e.,

y = 4, then new volume = 2 × 4 × 4 = 32 cu. units

If we increase z by 1 unit keeping the other same, i.e.,

z = 5, then new volume = 2 × 3 × 5 = 30 cu. units.

Hence the increase in volume is greatest, when x increases.

You can check with other values also.