Question

You are an engineer for a company that produces shipping boxes. The boxes that are made on one machine are all in the shape of a cube. As the demand for different size boxes changes you need to be able to change the setting on the machine so you can vary the side length of the cube shaped box. Draw a picture of a cube and label the cube's side length, s. Prior to placing your order for more cardboard, tape, packing material, etc. your boss asked you to determine each of the following: a. Write an expression to determine the surface area of a cube-shaped box, SA, in terms of its side length, s (in inches). SA Preview What are the units for SAP Select an answer
b. Define a formula to determine the volume of a cube-shaped box, V, in terms of its side length, s, (in inches). Preview What are the units for the cubes volume? Select an answer Given the formula for determining the volume of a 4 sphere is V = ar atrs, 3
a. Write the equation that you would solve to determine the radius of the sphere that has a volume of 87 cubic inches.
b. Evaluate the volume of the sphere when r = 5.9 inches. .
c. As the radius of the sphere increases from 2 to 4 inches, the volume of the sphere Select an answer from to_______

Answer 1

Answer:

Step-by-step explanation:

Draw a picture of a cube and label the cube's side length, s. Prior to placing your order for more cardboard, tape, packing material, etc. your boss asked you to determine each of the following: a. Write an expression to determine the surface area of a cube-shaped box, SA, in terms of its side length, s (in inches).

The surface area of a cube of side length s is A = 6s^2; there are 6 sides each of area s^2.

If s is measured in inches, then A = 6x^2 inches^2.

b. Define a formula to determine the volume of a cube-shaped box, V, in terms of its side length, s, (in inches). Preview What are the units for the cube's volume?

The formula for the volume of a cube is V = s^3.  In this case, V is measured in inches^3.

c.  Given the formula for determining the volume of a 4 sphere is V = ar atrs, 3 (This is incorrect; the formula in question, for the volume of a sphere of radius r is V = (4/3)(pi)r^3.           (1) We can solve this formula for r^3, and then for r:

                                                  3V

3V = 4(pi)r^3 becomes r^3 = ------------

                                                 4(pi)

and so the formula for the radius of a sphere whose volume is 87 inches^3

is

     ∛(3V)        ∛3*87 in^3

r = ------------ = ------------------

      ∛(4pi)        ∛(4pi)

(2) The volume of the sphere when r = 5.9 in is:

                                                     4(3.14)      205.38 in³

(4/3)(pi)r^3 = (4/3)(pi)(5.9 in)³  =   --------- = --------------------- = 67.46 in³

                                                         3                 3

         

(3) V = (4/3)(pi)r³    

     Please share the possible answer choices.  Basically, you must find the volume twice:  once for a radius of 4 in and once for a radius of 2 in.  Then subtract the smaller from the larger.  The numerical result is the desired answer.