Question

A spherical ball is measured to have a radius of 15 mm, with a possible measurement error of 0.1 mm. What is the possible change in volume (in mm³)?

a) 1,413 mm³
b) 4,710 mm³
c) 9,420 mm³
d) 14,130 mm³

Answer 1

The possible change in volume of the spherical ball is 6.4 mm³.

This correct answer is none of the above.

Step-by-step explanation:

To find the possible change in volume, we need to calculate the volume of the ball and the maximum and minimum possible radii of the ball.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Given that the radius of the ball is 15 mm with a possible measurement error of 0.1 mm, the maximum radius would be 15.1 mm and the minimum radius would be 14.9 mm.

Using the formula, we can calculate the volume with the maximum and minimum radii:

Maximum volume = (4/3)π(15.1 mm)³ = 14,133.1 mm³

Minimum volume = (4/3)π(14.9 mm)³ = 14,126.7 mm³

The possible change in volume is the difference between the maximum and minimum volumes:

Possible change in volume = 14,133.1 mm³ - 14,126.7 mm³ = 6.4 mm³

Therefore, the possible change in volume is 6.4 mm³.

This correct answer is none of the above.