Question

A new rectangular holding tank is being built. The tank's sides and bottom should be 1 foot thick. Its outer length should be twice its outer width and height.What should the outer dimensions of the tank be if it is to have a volume of 36 cubic feet? Use x for the outer width of the tank.

Answer 1

Answer: The tank is 4 feet high, 4 feet wide and 8 feet long.

Explanation:

From the statement "Its outer length should be twice its outer width and height.", we get that the width and height of rectangular tank is same.

let 'x' be the outer width of the tank.

then the outer height is also 'x' and the outer length will be 2x.

Since, the tank's sides and bottom should be 1 foot thick.

Therefore, the inner dimensions of rectangular tank will be

inner length =
`2x-2`

inner width =
`x-2`

inner height =
`x-1`

Also the volume of tank = 36 cubic feet

`\\\Rightarrow(2x-2)(x-2)(x-1)=36\\\Rightarrow2x^3-8x^2+10x-4=36\\\Rightarrow2x^3-8x^2+10x-40=0\\\Rightarrow2x^2(x-4)+10(x-4)=0\\\Rightarrow(2x^2+10)(x-4)=0\\\Rightarrow\ 2x^2=10\ or\ x=4\\\Rightarrow\ x^2=5\ or\ x=4`

The only real solution is x=4

Therefore, the outer width and height of the rectangular tank= 4 feet

The outer length= 2(4)=8 feet