Question

Все рёбра четырёхугольной пирамиды уменьшили в три раза. Во сколько раз уменьшился объём пирамиды?

Answer 1

Ответ:

Уменьшится в три раза,

Объяснение:

так как площадь основания не изменилась, а высота, равная боковому ребру уменьшилась в три раза.

Answer 2

Calculating the Decrease in Volume of a Pyramid

To calculate the decrease in volume of a pyramid when all its edges are reduced by three times, we can use the formula for the volume of a pyramid, which is given by:

V = (1/3) * A * h

Where: - V is the volume of the pyramid - A is the base area of the pyramid - h is the height of the pyramid

When all the edges of the pyramid are reduced by three times, the base area and height are also reduced by three times. Therefore, the new volume (V') can be calculated as:

V' = (1/3) * (A/9) * (h/3) V' = (1/27) * A * h

The decrease in volume can be calculated by finding the ratio of the new volume to the original volume:

Decrease in Volume = V / V' Decrease in Volume = 1 / (1/27) Decrease in Volume = 27

So, the volume of the pyramid decreases by a factor of 27 when all its edges are reduced by three times.