Question

Во сколько раз увеличиться объем шара , если его диаметр увеличить в 5 раз

Answer 1

Увеличится в 5³=125 раз
ответ в 125раз

Answer 2

Calculating the Increase in Volume of a Sphere

To calculate the increase in volume of a sphere when its diameter is increased by 5 times, we can use the formula for the volume of a sphere, which is given by:

V = (4/3) * π * r^3

Where: - V = volume of the sphere - π (pi) is a constant approximately equal to 3.14159 - r = radius of the sphere

Increase in Volume Calculation

When the diameter of the sphere is increased by 5 times, the radius will also increase by 5 times. Let's denote the original radius as r and the new radius as 5r.

The original volume of the sphere is given by: V = (4/3) * π * r^3

The new volume of the sphere with the increased diameter is given by: V' = (4/3) * π * (5r)^3

To find the increase in volume, we can calculate the ratio of the new volume to the original volume: Increase in Volume = V' / V

Calculation Result

By substituting the values into the formulas and simplifying, we find that the increase in volume of the sphere when its diameter is increased by 5 times is approximately 125 times the original volume.

This calculation is based on the formula for the volume of a sphere and the relationship between the original and new radius.