Question

Итальянский скульптор Микеланджело вырезал из мрамора свою знаменитую статую Давид наблюдая натурщика Высота Давида без учета постамента H-4,34м рост натурщика h-1,6м Плотность мрамора р-2,7г/см3.средняя плотность человеческого тела р-1,04г/см3 во сколько раз скульптура Давида оказалась тяжелее натурщика ?

Answer 1

Очевидно m=p*V
m~p*h^3
m1/m2=p1*H1^3/p2*h^3=p1/p2   *(H/h)^3=2.7/1,04*(4,34/1,04)^3=52

Answer 2

Calculation of Weight Discrepancy

To calculate how many times heavier the sculpture of David is compared to the model, we can use the formula:

Weight = Density x Volume

First, we need to find the volume of the sculpture and the model, and then we can compare their weights based on the given densities.

Volume of the Sculpture (V_s)

The volume of the sculpture can be calculated using the formula for the volume of a cylinder:

V_s = πr^2h

Where: - r = radius of the sculpture (half of the diameter) - h = height of the sculpture

Given: - Height of David without the pedestal (H) = 4.34 m - Radius of the sculpture (assuming it's roughly cylindrical) = diameter/2 - Density of marble (ρ) = 2.7 g/cm^3

Volume of the Model (V_m)

The volume of the model can be calculated using the same formula as above, with the height of the model (h) and the average density of the human body (ρ).

Given: - Height of the model (h) = 1.6 m - Density of the human body (ρ) = 1.04 g/cm^3

Calculation

Let's calculate the volume of the sculpture and the model using the given information and then compare their weights to find out how many times heavier the sculpture of David is compared to the model.