18. The mass of a solid can be found by multiplying the solid's density by the volume of space the solid takes up . If the density of cement is 3150kg/m^3 a. Determine the density of cement in units of g/cm^3 b. Create a linear equation for the mass,, in kg, of a block of cement as a function of its volume, in m^3 . Remember the density of cement is 3150kg/m^3

a. To convert the density of cement from \( \text{kg/m}^3 \) to \( \text{g/cm}^3 \), we use the following conversion factors:<br /><br />1 kg = 1000 g <br />1 m\(^3\) = 1000000 cm\(^3\)<br /><br />Given that the density of cement is 3150 kg/m\(^3\), we can convert it as follows:<br /><br />\[ <br />\text{Density in } \text{g/cm}^3 = 3150 \, \text{kg/m}^3 \times \frac{1000 \, \text{g}}{1 \, \text{kg}} \times \frac{1 \, \text{m}^3}{1000000 \, \text{cm}^3} <br />\]<br /><br />\[ <br />= 3150 \times \frac{1000}{1000000} \, \text{g/cm}^3 <br />\]<br /><br />\[ <br />= 3.15 \, \text{g/cm}^3 <br />\]<br /><br />b. The mass of a block of cement can be expressed as a linear function of its volume using the formula:<br /><br />\[ <br />\text{Mass} = \text{Density} \times \text{Volume} <br />\]<br /><br />Given that the density of cement is 3150 kg/m\(^3\), the equation for the mass \( M \) (in kg) as a function of the volume \( V \) (in m\(^3\)) is:<br /><br />\[ <br />M(V) = 3150 \times V <br />\]<br /><br />Thus, the linear equation is:<br /><br />\[ <br />M = 3150V <br />\]