A metal sphere has a mass of 1 kg. 1 cubic centimeter of this metal has a mass of 4.8 grams. find the radius. how do you work this out?
1kg/(4.8g/cm^3) = 208.333 cm^3
So, now you know that
4π/3 r^3 = 208.333
To determine the radius of the metal sphere, we need to use the given information about its mass and the mass of the metal per unit volume.
Let's break down the problem step by step:
Step 1: Convert the mass of the sphere from kg to grams.
Since 1 kg is equal to 1000 grams, the mass of the sphere is 1000 grams.
Step 2: Find the volume of the sphere.
We know that the mass of 1 cm³ of the metal is 4.8 grams. Therefore, the mass of the sphere (1000 grams) is also equal to the mass per unit volume multiplied by the volume of the sphere:
1000 grams = 4.8 grams/cm³ * V cm³
To isolate V, divide both sides by 4.8 grams/cm³:
V cm³ = 1000 grams / 4.8 grams/cm³
Step 3: Calculate the radius of the sphere.
The volume of a sphere can be found using the formula:
V = (4/3) * π * r³, where V is the volume and r is the radius.
Rearranging this equation to solve for r, we have:
(4/3) * π * r³ = V cm³
Substituting the value of V from step 2, we get:
(4/3) * π * r³ = 1000 grams / 4.8 grams/cm³
Simplifying further:
(4/3) * π * r³ = 208.33 cm³
Divide both sides by (4/3) * π, and take the cube root to solve for r:
r = (208.33 cm³ / (4/3) * π)^(1/3)
Now, you can evaluate this expression using a calculator to find the radius of the metal sphere.