Question

The weight of a sphere is proportional to its radius cubed. If a sphere of diameter 1 cm has a mass of 10 grams, what diameter sphere has a mass of 640grams?

Answer 1

To find the diameter of a sphere with a given mass, we use the proportionality between weight and radius cubed. By solving a proportionality equation, we can determine the diameter of the sphere with a mass of 640 grams.

Step-by-step explanation:

To find the diameter of a sphere with a mass of 640 grams, we can use the proportionality between weight and radius cubed. Since weight is proportional to radius cubed, we have the equation
`w = k * r^3`, where w is the weight, r is the radius, and k is the proportionality constant.

Given that a sphere with a diameter of 1 cm has a mass of 10 grams, we can calculate the proportionality constant. Since the diameter is equal to 2 times the radius, we have 2 * r = 1 cm, which implies r = 1/2 cm. Plugging these values into the equation, we can solve for k:
`10 = k * (1/2)^3`. Simplifying, we find k = 80.

Now, to find the diameter of the sphere with a mass of 640 grams, we can solve the equation
`640 = 80 * r^3`. Dividing both sides by 80 and taking the cube root, we find r =
`(640/80)^{(1/3)` = 2 cm. Since the diameter is equal to 2 times the radius, the diameter of the sphere with a mass of 640 grams is 4 cm.

Answer 2

if 1cm-10grams

what Abt 640 grams=64cm