The volume of a sphere is 972 pie in cubic inches. what is the radius

Hope that's an apple pie. Just between us, we want to discuss pi, or , or π, not pie.

The formula for the volume of a sphere of radius r is V = (4π/3)*r^3. Since we know that V = 972π, we know that 972π = (4π/3)r^3.

We must solve for r^3, and then solve for r.

To accomplish this, multiply both sides of the equation by 3 / (4π). This results in the equation

(3) 972π

----- * --------- = 729 = r^3.

4π 1

Taking the cube root of both sides of this result, we get r = 9.

The radius of this sphere is 9 units.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

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step-by-step explanation: