Question

A toy manufacturer has designed a new piece for use in building models. It is a cube with side length 7m and it has a 3m diameter circular hole cut through the middle. The manufacture wants 1,000,000 prototypes. If the plastic used to creat the piece cost $280 per cubic meter, how much will the prototype cost? round to the nearest million dollar.

Answer 1

79,257,000,000 dollars.

Step-by-step explanation:

We first need to calculate the volume of the piece. This volume is equal to the volume of the cube less the volume of the cylinder.

The volume of the cube is equal to

Vcube = side x side x side

Vcube = 7 m x 7 m x 7 m

Vcube = 343 m³

The volume of the cylinder is

Vcylinder = πr²h

Where π = 3.14, r is the radius and h is the height, which is 7 m. The radius is half the diameter, so

diameter = radius/2

diameter = 3 m / 2

diameter = 1.5 m

Then, the volume of the cylinder is

Vcylinder = (3.14)(1.5 m)²(7 m)

Vcylinder = 49.455 m³

Therefore, the volume of the piece is equal to

Vpiece = 343 m³ - 49.455 m³

Vpiece = 293.545 m³

Then, they want 1,000,000 prototypes with a cost of $270 per cubic meter, so the total cost is equal to

$270 x 293.545 m³ x 1,000,000 = $79,257 x 10⁶

Therefore, the prototype cost to the nearest million dollars is

79,257,000,000 dollars.