Question

A company is desinging a square prism. Its height is 3 yarss longer than a side of its base. The volume of the prism must be 20 cubic yards. Write a representative function for the volune of the solid..

Answer 1

`a^(2) (a+3) = 20\\OR\\a^3 +3a^2 -20 = 0`

Explanation:

Given that:

There is a square prism which has height equal to 3 yards longer than that of the base of the prism.

Let the base of prism =
`a` units

As per question statement:

Height,
`h = (a+3)` units

Volume of the prism = 20 cubic yards

Now, we have to find a representative function that will represent the volume of the solid.

First of all, let us have a look at the formula for volume of a prism.

`V = B* h`

Where,
`B` is the area of base and

`h` is the height of prism.

And the base is a square, whose area will be represented as:

`B = Side * Side`

Now, putting the values in the formula for Volume:

`V = a^2(a+3) = 20\\OR\\a^3+3a - 20 =0`