Question

A pyramid has a square base of side x metres. The perpendicular height of the pyramid is 6 cm longer than the perimeter of its base. If the volume of the pyramid is to be 54 cm3, write a polynomial equation to represent this information and, by solving the equation, find the dimensions of the pyramid.

Answer 1

To find the dimensions of the pyramid and write the polynomial equation, we use the fact that the base is a square and the height is 6 cm longer than the perimeter of the base. Using the volume formula, we can set up the equation (4/3) * (x^3) + (2x^2) - 54 = 0 and solve for x.

Step-by-step explanation:

To write the polynomial equation representing the given information, let's first find the dimensions of the pyramid.

Given that the base of the pyramid is a square with side length x metres, the perimeter of the base would be 4x metres. The height of the pyramid is 6 cm longer than the perimeter of its base, so it would be (4x + 6) cm.

The volume of a pyramid is given by the formula V = (1/3) * (base area) * height. Plugging in the values, we have (1/3) * (x^2) * (4x + 6) = 54 cm3.

This equation can be simplified to (4/3) * (x^3) + (2x^2) - 54 = 0, which represents the polynomial equation.

To solve this equation, you can use various algebraic methods like factoring, synthetic division, or the quadratic formula. The solution for x will give you the dimensions of the pyramid.