Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B? [Volume of a sphere of radius r is given by V = 4ðr63/3]
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To solve this problem, we can use the fact that the mass of an object is directly proportional to its volume. Since spheres A and B are made from the same material, we can equate their volumes to find the relationship between their radii.
The volume of a sphere is given by the formula V = 4/3 * π * r^3, where r is the radius.
Let's calculate the volume of sphere A using its given radius:
V_A = 4/3 * π * (7.50 cm)^3
Now, we know that the mass of sphere B is eight times that of sphere A. Since mass is directly proportional to volume, we can write the proportion as follows:
V_B / V_A = 8
Substituting the volume expressions, we get:
(4/3 * π * r_B^3) / (4/3 * π * (7.50 cm)^3) = 8
Now we can simplify and solve for the radius of sphere B:
r_B^3 / (7.50 cm)^3 = 8/1
r_B^3 = (8/1) * (7.50 cm)^3
Taking the cube root of both sides, we find:
r_B = ∛[(8/1) * (7.50 cm)^3]
Calculating this expression will give us the value of the radius of sphere B.