Question

Чугунный шар имеет массу 4,2 кг при объеме 700см ³ . Найдите объем полости в шаре.

Answer 1

Если плотность чугуна p=7 г\см3


Vч=m\p=4200\7=600 см3


V0=700-600=100 см3 - объем полости

Answer 2

Calculating the Volume of the Cavity in the Iron Sphere

To find the volume of the cavity in the iron sphere, we can use the formula for the volume of a sphere and the given mass and volume.

Given: - Mass of the iron sphere = 4.2 kg - Volume of the iron sphere = 700 cm³

We can use the formula: \[ V = \frac{4}{3} \pi r^3 \] where V is the volume of the sphere and r is the radius of the sphere.

Calculating the Radius of the Iron Sphere

First, we need to calculate the radius of the iron sphere using the given volume.

\[ V = \frac{4}{3} \pi r^3 \] \[ r^3 = \frac{3V}{4\pi} \] \[ r = \sqrt[3]{\frac{3V}{4\pi}} \]

Substitute the given volume: \[ r = \sqrt[3]{\frac{3 \times 700}{4 \times \pi}} \]

Calculating the value of r: \[ r \approx 6.29 \, \text{cm} \]

Calculating the Volume of the Cavity

The volume of the cavity in the iron sphere can be calculated using the formula for the volume of a sphere and the radius of the sphere.

The formula for the volume of the cavity in a sphere is: \[ V_{\text{cavity}} = V_{\text{sphere}} - V_{\text{solid}} \] where \( V_{\text{sphere}} \) is the volume of the sphere and \( V_{\text{solid}} \) is the volume of the solid material inside the sphere.

Given: - Volume of the iron sphere = 700 cm³ - Radius of the iron sphere = 6.29 cm

Using the formula: \[ V_{\text{cavity}} = \frac{4}{3} \pi r^3 - 700 \]

Calculating the volume of the cavity: \[ V_{\text{cavity}} \approx 2.53 \, \text{cm}^3 \]

The volume of the cavity in the iron sphere is approximately 2.53 cm³.