A closed rectangular prism has a square bottom. The lengths of the edges all 12 edges add up to 200 cm. Write the volume of the prism in terms of q, q being the being one of the edges of the bottom.

Expert Answers
justaguide eNotes educator| Certified Educator

The closed rectangular prism has a square base. The length of all the 12 edges adds up to 200 cm. The edge at the bottom is represented by q. As the rectangle has a square base this gives two of the sides equal to q and the third side equal to `(200 - 8q)/4`

The volume of the prism is `q*q*(200 - 8q)/4`

= `(50 - 2q)*q^2`

=> `50q^2 - 2q^3`

The volume of the pyramid is given by the expression: `50q^2 - 2q^3`