You should come up with the following substitution for the length of the side of square such that:

`l = x`

You need to evaluate the volume of rectangular block of wood such that:

`V = 24x^2`

The ornament is formed from two spheres and two cubes, hence, the volume...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

You should come up with the following substitution for the length of the side of square such that:

`l = x`

You need to evaluate the volume of rectangular block of wood such that:

`V = 24x^2`

The ornament is formed from two spheres and two cubes, hence, the volume of ornament may be evaluated such that:

`V_1 = 2V_s + 2V_c`

You need to evaluate the volume of the sphere, using the provided information, such that:

`V_s = (4/3)pi*x^3`

You need to evaluate the volume of cube such that:

`V_c = x^3`

`(4/3)pi*x^3 + x^3 = 24x^2 => x^3*(4/3 pi + 1) = 24 x^2`

`x = 24/(4/3 pi + 1)`

`V_1 = (8/3)pi*(24/(4/3 pi + 1))^3 + (24/(4/3 pi + 1))^3`

**Hence, evaluating the volume of ornament yields `V_1 = (8/3)pi*(24/(4/3 pi + 1))^3 + 2*(24/(4/3 pi + 1))^3.` **