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21 Jackson is trying to find the density, in g/cm^3 of a block of wood. The block of wood is in the shape of a cuboid. He measures the length as 132 cm, correct to the nearest mm the width as 16.0 cm, correct to the nearest mm the height as 21,7 cm, correct to the nearest mm He measures the mass as 1970 g, correct to the nearest 5 g By considering bounds work out the density of the wood. Give your answer to a suitable degree of accuracy. You must show all your working and give a reason for your final answer.

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21 Jackson is trying to find the density, in g/cm^3 of a block of wood. The block of wood is in the shape of a cuboid. He measures the length as 132 cm, correct to the nearest mm the width as 16.0 cm, correct to the nearest mm the height as 21,7 cm, correct to the nearest mm He measures the mass as 1970 g, correct to the nearest 5 g By considering bounds work out the density of the wood. Give your answer to a suitable degree of accuracy. You must show all your working and give a reason for your final answer.

21 Jackson is trying to find the density, in g/cm^3 of a block of wood. The block of wood is in the shape of a cuboid. He measures the length as 132 cm, correct to the nearest mm the width as 16.0 cm, correct to the nearest mm the height as 21,7 cm, correct to the nearest mm He measures the mass as 1970 g, correct to the nearest 5 g By considering bounds work out the density of the wood. Give your answer to a suitable degree of accuracy. You must show all your working and give a reason for your final answer.

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XavierMaster · Tutor for 5 years

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### The density of the wood is approximately \(0.430 \, \text{g/cm}^3\).

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## Step 1: Determine the bounds for each measurement<br />### The length, width, height, and mass are given with their respective precisions. We need to calculate the upper and lower bounds for each measurement.<br />- Length: \(13.2 \pm 0.05\) cm<br />- Width: \(16.0 \pm 0.05\) cm<br />- Height: \(21.7 \pm 0.05\) cm<br />- Mass: \(1970 \pm 2.5\) g<br /><br />## Step 2: Calculate the volume bounds<br />### Using the bounds for length, width, and height, we calculate the minimum and maximum possible volumes.<br />- Minimum volume: \((13.15 \, \text{cm}) \times (15.95 \, \text{cm}) \times (21.65 \, \text{cm})\)<br />- Maximum volume: \((13.25 \, \text{cm}) \times (16.05 \, \text{cm}) \times (21.75 \, \text{cm})\)<br /><br />## Step 3: Compute the volume values<br />### Calculate the minimum and maximum volumes using the bounds.<br />- Minimum volume: \(13.15 \times 15.95 \times 21.65 \approx 4538.76 \, \text{cm}^3\)<br />- Maximum volume: \(13.25 \times 16.05 \times 21.75 \approx 4624.59 \, \text{cm}^3\)<br /><br />## Step 4: Calculate the density bounds<br />### Using the bounds for mass and the calculated volumes, determine the minimum and maximum densities.<br />- Minimum density: \(\frac{1967.5 \, \text{g}}{4624.59 \, \text{cm}^3} \approx 0.425 \, \text{g/cm}^3\)<br />- Maximum density: \(\frac{1972.5 \, \text{g}}{4538.76 \, \text{cm}^3} \approx 0.434 \, \text{g/cm}^3\)<br /><br />## Step 5: Determine the suitable degree of accuracy<br />### Given the precision of the measurements, the density should be reported to three decimal places, as the variations are in the third decimal place.
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