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.
