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]
Assumeing density is the same.
MassA=density*4/3 PI ra^3
MassB= density*4/3 PI rb^3
divideing the second by the first
8=(rb/ra)^3 It sure looks like the ratio of rb/ra is 2.
check my work.
To find the radius of sphere B, we need to use the given information about the mass of the spheres.
First, let's find the mass of sphere A.
The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
The mass of a sphere is directly proportional to its volume and the density of the material it's made of. However, since both spheres are made from the same material and we are not given the density of the material, we can ignore it for this problem.
Let's denote the mass of sphere A as mA and the mass of sphere B as mB. Since sphere B has eight times the mass of A, we can express this relationship as:
mB = 8mA
Now, let's find the volume of sphere A using its given radius:
V = (4/3)πr³
mA = (4/3)π(7.50 cm)³
Next, let's find the volume of sphere B. Since sphere B is made from the same material as A, its density is the same. Therefore, it obeys the same relationship of mass and volume:
mB = (4/3)π(rB)³
We can substitute the mass relationship between the spheres into this equation:
8mA = (4/3)π(rB)³
Now, let's solve for the radius of sphere B:
8mA = (4/3)π(rB)³
Divide both sides by (4/3)π:
8mA / [(4/3)π] = (rB)³
Simplify the left side:
(8mA * 3) / (4π) = (rB)³
Multiply (8 * 3) and divide by 4:
24mA / π = (rB)³
Cube root both sides to solve for rB:
rB = ∛(24mA / π)
Now that we know the mass of sphere A and have substituted it into the equation, we can calculate the radius of sphere B.