# Increase in cube dimension

One dimension of a cube is increased by 1 inches to form a rectangular block. Suppose that the volume of the new block is 150 cubic inches. find the length of an edge of the original cube.

http://solvemaths.in/increase-in-cube-dimension/ArithmeticContestOne dimension of a cube is increased by 1 inches to form a rectangular block. Suppose that the volume of the new block is 150 cubic inches. find the length of an edge of the original cube.

rammsah30@a2plcpnl0464.prod.iad2.secureserver.netAdministratorSOLVE - ΜΔΓΗŠ
ANSWER= The length of an edge of original cube = 5 inch

Let the original dimension be lxlxl

Increase one dimension by 1 unit. New dimension : (l+1)xlxl

New volume = (l+1)*l*l

or, 150 = l^3 + l^2

or, l^3 + l^2 – 150 = 0 —— (i)

To solve this equation, we assume the first root of the eqn:

Let l = 1, eqn doesn’t satisfy

Let l = 2, eqn doesn’t satisfy

Let l = 3, eqn doesn’t satisfy

Let l = 4, eqn doesn’t satisfy

Let l = 5, 5^3 + 5^2 – 150 => 125 + 25 – 150 => 0 => Eqn satsfies.

Therefore, l = 5 is the answer.