What is the volume of a sphere with a diameter the same length as the side of a cube with a volume of 27 cubic inches?

volume ≈ 14.14 in³

Step-by-step explanation:

Given the volume of a cube = 27 = s³ ( s is the side length ), then

s = = 3

diameter of sphere = 3 ⇒ r = = 1.5

The volume (V) of a sphere is calculated using the formula

V = πr³

  = ≈ 14.14 in³ ( 2 dec. places )

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

step-by-step explanation: