Spheres A and B are similar.
The volume of Sphere A x 64 = the volume of Sphere B
How many times greater is the radius of sphere A? (This is called the scale factor.)
a
16
b
8
c
4
d
64
b
8
To find the scale factor between the two spheres, we need to compare the radii of Sphere A and Sphere B.
Let's assume the radius of Sphere A is r.
According to the given information, the volume of Sphere A multiplied by 64 is equal to the volume of Sphere B. Since the volumes of spheres are proportional to the cube of their radii, we can set up the following equation:
(r^3) x 64 = (r^3)
Simplifying the equation, we have:
64r^3 = r^3
Divide both sides of the equation by r^3 to isolate the scale factor:
64 = 1
This equation is not possible since 64 cannot equal 1.
Therefore, there seems to be an error or inconsistency in the information provided. Please double-check the given details or provide additional information.
To find the scale factor, we need to compare the radii of Sphere A and Sphere B since they are similar spheres.
Let's assume the radius of Sphere A is 'r'. According to the problem, the volume of Sphere A multiplied by 64 is equal to the volume of Sphere B.
The volume of a sphere is given by the formula V = (4/3)πr³.
So, the volume of Sphere A can be expressed as (4/3)π(r^3), and the volume of Sphere B is (4/3)π((kr)^3), where 'k' represents the scale factor.
Using the given information, we can write the equation:
(4/3)π(r^3) * 64 = (4/3)π((kr)^3)
Simplifying, we can cancel out the common terms and solve for 'k':
64(r^3) = (kr)^3
Taking the cube root of both sides, we get:
4r = kr
Now, we can cancel out the 'r' terms and solve for 'k':
4 = k
Hence, the scale factor, or the number of times greater the radius of Sphere A is compared to Sphere B, is 4.
Therefore, the correct answer is c) 4.