Question

Медный шар, в котором имеется воздушная полость, опущен в керосин. Наружный объём шара 0,1 м3. Найдите объём воздушной полости, если шар плавает на поверхности керосина, погрузившись в него на 0,89 своего объёма.

Answer 1

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Answer 2

Calculation of the Volume of the Air Cavity in the Copper Ball

To find the volume of the air cavity in the copper ball, we can use the given information that the ball floats on the surface of kerosene and sinks into it to a depth of 0.89 times its own volume.

Let's assume the volume of the air cavity in the copper ball is V_air, and the total volume of the ball is V_total.

According to the given information, the ball sinks into the kerosene to a depth of 0.89 times its own volume. This means that the volume of kerosene displaced by the ball is 0.89 times V_total.

Since the ball floats on the surface of the kerosene, the volume of kerosene displaced by the ball is equal to the volume of the ball itself. Therefore, we can write the equation:

V_air + V_kerosene = V_total

Substituting the given information, we have:

V_air + 0.89 * V_total = V_total

Simplifying the equation, we find:

V_air = 0.11 * V_total

Since the given information states that the external volume of the ball is 0.1 m^3, we can substitute V_total with 0.1 m^3:

V_air = 0.11 * 0.1 m^3

Calculating the volume of the air cavity, we find:

V_air = 0.011 m^3

Therefore, the volume of the air cavity in the copper ball is 0.011 m^3.