Find dimesnsions of rectangular prism with V=6y^3+11y^2+3y

Question

I have an algebra question and all I could find from this was V=340y however it needs more than one possible solution

Answer 1

You know that volume is the product of the dimensions of 3 sides.  But first, we need to set up the equation represented by the volume.

 

340y = 6y³ + 11y² + 3y

 

 

Subtract 340y on both sides of the equation.

 

0 = 6y³ + 11y² - 337y

 

0 = y(6y² + 11y - 337)

 

 

Now set the factor equal to each other.

 

y = 0                     6y² + 11y - 337 = 0

 

 

Since length cannot be zero nor negative, we reject y=0.

 

Use the quadratic formula to solve the quadratic factor.  You will have two values of y.  Plug them into the quadratic factor to get the dimensions.