A ball of radius 100 was melted into balls of radius 10. One of them was melted

| September 4, 2021 | education

A ball of radius 100 was melted into balls of radius 10. One of them was melted into balls of radius 1. Which balls are larger: radius 10 or radius 1?

Let’s use the formula to find the volume of the ball V = ¾ * π * R3.

The volume of a sphere of radius 100 is V100 = ¾ * π * 100 ^ 3.

The volume of a sphere of radius 10 is V10 = ¾ * π * 10 ^ 3.

Let us determine the number of balls of radius 10, which will be obtained after melting from a ball of radius 100.

V100 / V10 = (¾ * π * 100 ^ 3) / (¾ * π * 10 ^ 3) = 100 ^ 3/10 ^ 3 = 1,000,000 / 1,000 = 1,000.

The volume of a ball of radius 1 is V1 = ¾ * π * 13 = ¾ * π.

Let us determine the number of balls of radius 1 obtained from a ball of radius 10.

V10 / V1 = (¾ * π * 10 ^ 3) / (¾ * π) = 10 ^ 3 = 1000.

Because balls of radius 1 were melted from one ball of radius 10, then there are (1000 – 1) = 999 of them.

Those. As a result, 999 balls of radius 10 and 1000 balls of radius 1 remain.

Answer: more balls of radius 1.



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