Sure! Let's tackle each of these questions step by step.
### Question 1
Calculate the mass of 8 m³ of cement of density 2000 kg/m³.
To find the mass of the cement, you can use the formula:
[tex]\[ \text{mass} = \text{volume} \times \text{density} \][/tex]
Given:
- Volume of cement, [tex]\( V = 8 \)[/tex] m³
- Density of cement, [tex]\( \rho = 2000 \)[/tex] kg/m³
Substitute the given values into the formula:
[tex]\[ \text{mass} = 8 \, \text{m}³ \times 2000 \, \text{kg/m}³ = 16000 \, \text{kg} \][/tex]
So, the mass of 8 m³ of cement is 16000 kg.
### Question 2
Calculate the density of a 2[tex]\(\times\)[/tex]5[tex]\(\times\)[/tex]8 cm³ block of mass 800 g.
First, find the volume of the block:
[tex]\[ \text{volume} = \text{length} \times \text{width} \times \text{height} \][/tex]
[tex]\[ \text{volume} = 2 \, \text{cm} \times 5 \, \text{cm} \times 8 \, \text{cm} = 80 \, \text{cm}³ \][/tex]
Convert the volume from cm³ to m³:
[tex]\[ 1 \, \text{cm}³ = 1 \times 10^{-6} \, \text{m}³ \][/tex]
[tex]\[ \text{volume in m}³ = 80 \, \text{cm}³ \times 1 \times 10^{-6} \, \text{m}³/\text{cm}³ = 8 \times 10^{-5} \, \text{m}³ \][/tex]
Convert the mass from grams to kilograms:
[tex]\[ 1 \, \text{g} = 1 \times 10^{-3} \, \text{kg} \][/tex]
[tex]\[ \text{mass in kg} = 800 \, \text{g} \times 1 \times 10^{-3} \, \text{kg/g} = 0.8 \, \text{kg} \][/tex]
Now, use the formula for density:
[tex]\[ \text{density} = \frac{\text{mass}}{\text{volume}} \][/tex]
[tex]\[ \text{density} = \frac{0.8 \, \text{kg}}{8 \times 10^{-5} \, \text{m}³} = 10000 \, \text{kg/m}³ \][/tex]
So, the density of the block is 10000 kg/m³.
### Question 3
If the mass of an object of density 500 kg/m³ is 50 kg, calculate its volume.
To find the volume, you can use the formula:
[tex]\[ \text{volume} = \frac{\text{mass}}{\text{density}} \][/tex]
Given:
- Density of the object, [tex]\( \rho = 500 \)[/tex] kg/m³
- Mass of the object, [tex]\( m = 50 \)[/tex] kg
Substitute the given values into the formula:
[tex]\[ \text{volume} = \frac{50 \, \text{kg}}{500 \, \text{kg/m}³} = 0.1 \, \text{m}³ \][/tex]
So, the volume of the object is 0.1 m³.
