Question

A rectangular block with a square base has total surface area 160000 mm^2, and the sides of the base are each x mm long. Prove that the volume of the block is 1/2 (80000x - x^3 ) mm^3. Hence find the maximum volume of the block.

Answer 1

Answer:

A solid rectangular block has a base which measures 2x2x cm by xx cm. The height of the block is yy cm and the volume of the block is 72cm372cm3. Express yy in terms of xx and show that the total surface area, Acm2Acm2 , of the block is given by

A=4x2+216x

A=4x2+216x

My attempt,

2x2y=722x2y=72

y=36x2y=36x2

A=2⋅2x2+4yxA=2⋅2x2+4yx

A=4x2+144x