How many times will the volume of the sphere decrease if its radius decreases 7 times?

Let us determine how many times the volume of the sphere will decrease if its radius decreases by 7 times.

1) First, we write down the formula for the volume of the ball.

V = 4/3 * pi * r ^ 3;

2) r / 7 – the radius, after it has been reduced by 7 times.

3) Find the volume of the ball, after changing the radius.

Vmeas = 4/3 * pi * (r / 7) ^ 3 = 4/3 * pi * (r ^ 3/7 ^ 3) = 4/3 * pi * r ^ 3 * 1/343;

4) Find the ratio of the volume of the ball before the change and after the change.

V / V meas = 4/3 * pi * r ^ 3 / (4/3 * pi * r ^ 3 * 1/343) = 1 / (1 * 1/343) = 1 / (1/343) = 343 /one.

From here we see that if the radius of the ball is reduced by 7 times, then the volume of the ball will decrease by 343 times.