Question

Радиус основания цилиндра увеличили в 9 раз, а высоту уменьшили в 3 раза. Во сколько раз увеличился объем цилиндра? Ответ

Answer 1

Ответ:

В 27раз.

Пошаговое объяснение:

Answer 2

Ответ:

Пошаговое объяснение:

Объём цилиндра вычисляется по формуле V=π⋅R2⋅H

по условию  радиус увеличили в 9 раз , а высоту уменьшили в 3 раза, получаем: V=π⋅ 9R2⋅(H/3)= π⋅3R2⋅H

Объем цилиндра увеличился в 3 раза

Answer 3

Calculation of the Volume of a Cylinder

To find the ratio by which the volume of a cylinder increases when the radius of the base is increased by 9 times and the height is decreased by 3 times, we need to understand the formula for the volume of a cylinder.

The formula for the volume of a cylinder is:

V = π * r^2 * h

Where: - V is the volume of the cylinder - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

Changes in the Dimensions of the Cylinder

According to the given information, the radius of the base of the cylinder is increased by 9 times, and the height is decreased by 3 times.

Let's assume the original radius of the cylinder is r and the original height is h.

After the changes, the new radius becomes 9r and the new height becomes h/3.

Calculation of the New Volume

Substituting the new values into the volume formula, we can calculate the new volume of the cylinder:

V_new = π * (9r)^2 * (h/3)

Simplifying the equation:

V_new = π * 81r^2 * (h/3)

V_new = 27π * r^2 * h

Comparison of the New and Original Volumes

To find the ratio by which the volume of the cylinder increased, we can divide the new volume by the original volume:

Ratio = V_new / V_original

Substituting the formulas for the new and original volumes:

Ratio = (27π * r^2 * h) / (π * r^2 * h)

Simplifying the equation:

Ratio = 27

Therefore, the volume of the cylinder increases by a factor of 27 when the radius of the base is increased by 9 times and the height is decreased by 3 times.

Please let me know if you need any further clarification.