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6. A cube has a side length of 4 inches and a mass of 5 lbs Use the conversion rates below to find the density of the cube in kg/m^3 1inch=25mm 1lb=450g [4 marks] Answer kg/m^3

Question

6. A cube has a side length of 4 inches and a
mass of 5 lbs
Use the conversion rates below to find the
density of the cube in kg/m^3
1inch=25mm
1lb=450g
[4 marks]
Answer
kg/m^3

6. A cube has a side length of 4 inches and a mass of 5 lbs Use the conversion rates below to find the density of the cube in kg/m^3 1inch=25mm 1lb=450g [4 marks] Answer kg/m^3

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SidneyProfessional · Tutor for 6 years

Answer

### 2250 \(\mathrm{kg} / \mathrm{m}^{3}\)

Explain

## Step 1: Convert the side length from inches to meters<br />### The side length of the cube is 4 inches. Convert this to meters using the given conversion rate \(1 \text{ inch} = 25 \text{ mm}\).<br />\[4 \text{ inches} \times 25 \text{ mm/inch} = 100 \text{ mm}\]<br />Convert millimeters to meters:<br />\[100 \text{ mm} = 0.1 \text{ m}\]<br /><br />## Step 2: Calculate the volume of the cube in cubic meters<br />### The volume \(V\) of a cube is given by \(V = s^3\), where \(s\) is the side length.<br />\[V = (0.1 \text{ m})^3 = 0.001 \text{ m}^3\]<br /><br />## Step 3: Convert the mass from pounds to kilograms<br />### The mass of the cube is 5 lbs. Convert this to grams using the given conversion rate \(1 \text{ lb} = 450 \text{ g}\).<br />\[5 \text{ lbs} \times 450 \text{ g/lb} = 2250 \text{ g}\]<br />Convert grams to kilograms:<br />\[2250 \text{ g} = 2.25 \text{ kg}\]<br /><br />## Step 4: Calculate the density in \(\mathrm{kg} / \mathrm{m}^{3}\)<br />### Density \(\rho\) is given by \(\rho = \frac{M}{V}\), where \(M\) is the mass and \(V\) is the volume.<br />\[\rho = \frac{2.25 \text{ kg}}{0.001 \text{ m}^3} = 2250 \text{ kg/m}^3\]
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