Given two balls. The radius of the first ball is 2 times the radius of the second.

| April 25, 2021 | education

Given two balls. The radius of the first ball is 2 times the radius of the second. How many times is the volume of the first ball greater than the volume of the second?

1. Let’s designate the radius of the second ball R. The volume of the ball of radius R is calculated by the formula:

V = (4/3) * pi * R ^ 3.

2. This means that the volume of a sphere of radius 2R will be calculated by the formula:

V2 = (4/3) * pi * (2R) ^ 3.

3. Let’s open the brackets, then we get:

V2 = (4/3) * pi * (2R) ^ 3 = (4/3) * pi * 8 * R ^ 3 = 8 * ((4/3) * pi * R ^ 3) = 8 * V.

4. From here it can be seen that the volume of the first ball is 8 times greater than the volume of the second ball.

Answer: the volume of the first ball is 8 times greater than the volume of the second ball.



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