An irregularly shaped chunk of concrete has a hollow spherical cavity inside. The mass of the chunk is 32kg, and the volume enclosed by the outside surface of the chunk is 0.020m^3. What is the radius of the spherical cavity?

To solve this, you need to know the density of concrete without the hole. The internet gives a range of values, mostly from 2300 to 2500 kg/m^3. Call that density "rho".

If R is the radius of the spherical cavity inside,
[0.020 m^3 - (4/3)pi R^3]*(rho) = 32 kg
I suggest you use 2400 kg/m^3 for "rho" and solve for R.
48 - 32 = 16 = (4/3)pi*R^3*2400

R^3 = 16/2400pi

R = 0.25 m

To find the radius of the spherical cavity, we can rearrange the equation:

(4/3)πR^3 = (48 - 32) / (2400 * π)

Simplifying the equation further:

(4/3)πR^3 = 16 / (2400 * π)
R^3 = 16 / (2400 * 3)
R^3 = 16 / 7200
R^3 = 1 / 450

To find the radius, we need to take the cube root of both sides:

R = (1 / 450)^(1/3)
R ≈ 0.0792 meters (rounded to 4 decimal places)

Therefore, the radius of the spherical cavity is approximately 0.0792 meters.

To find the radius of the spherical cavity, you can rearrange the equation that was derived earlier.

First, divide both sides of the equation by (4/3)pi*2400:

16/((4/3)pi*2400) = R^3

Next, simplify the equation:

16/(4/3)pi*2400 = R^3

Multiply both sides of the equation by (4/3)pi*2400:

R^3 = (16/(4/3)pi*2400)

Take the cube root of both sides of the equation to isolate R:

R = (16/(4/3)pi*2400)^(1/3)

Now, you can use a calculator to evaluate the right side of the equation and find the value of R.