AskSia

Plus

现有由同种材料制成的A、B两金属球，其中一个是实心的。它们的质量分别为128g、60g，体积分别为16立方厘米、12立方厘米。针对A、B两球求出： ①空心球空...

Mar 19, 2024

现有由同种材料制成的A、B两金属球，其中一个是实心的。它们的质量分别为128g、60g，体积分别为16立方厘米、12立方厘米。针对A、B两球求出： ①空心球空心部分的体积是______立方厘米； ②体积是60cm3的A金属球它的质量是______kg。

Solution

Calculate the density of the solid sphere (A) using its mass and volume

$$ \rho_A = \frac{m_A}{V_A} = \frac{128 \text{ g}}{16 \text{ cm}^3} = 8 \text{ g/cm}^3 $$

Calculate the density of the hollow sphere (B) using its mass and volume

$$ \rho_B = \frac{m_B}{V_B} = \frac{60 \text{ g}}{12 \text{ cm}^3} = 5 \text{ g/cm}^3 $$

Since A and B are made of the same material, their densities should be equal. Use the density of A to find the volume of the hollow part of B

$$ V_{\text{hollow}} = V_B - \frac{m_B}{\rho_A} = 12 \text{ cm}^3 - \frac{60 \text{ g}}{8 \text{ g/cm}^3} = 4.5 \text{ cm}^3 $$

Calculate the mass of a solid sphere A with a volume of 60 cm³ using the density of A

$$ m_{A_{60cm^3}} = \rho_A \times 60 \text{ cm}^3 = 8 \text{ g/cm}^3 \times 60 \text{ cm}^3 = 480 \text{ g} = 0.480 \text{ kg} $$

Answer

①空心球空心部分的体积是4.5立方厘米；②体积是60cm³的A金属球它的质量是0.480kg

Key Concept

Density and its relation to mass and volume:

\rho = \frac{m}{V}

Explanation

The density of a material is constant, so we can use the density of one object to find the mass or volume of another object made of the same material.