The diagram shows a box in the shape of a cuboid. Diagram NOT accurately drawn The box is put on a table. The face of the box in contact with the table has length 1.2 metres and width a metres. The force exerted by the box on the table is 27 newtons. The pressure on the table due to the box is 30newtons/m^2 pressure=(force)/(area) Work out the value of x. (3 marks)

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The diagram shows a box in the shape of a cuboid. Diagram NOT accurately drawn The box is put on a table. The face of the box in contact with the table has length 1.2 metres and width a metres. The force exerted by the box on the table is 27 newtons. The pressure on the table due to the box is 30newtons/m^2 pressure=(force)/(area) Work out the value of x. (3 marks)

Answer 1

\(x = 0.75m\)

Answer 2

## Step 1: The problem provides the formula for pressure which is given as: ### \(\textbf{Pressure} = \frac{\textbf{Force}}{\textbf{Area}}\) The force exerted by the box on the table is given as 27 newtons and the pressure on the table due to the box is 30 newtons/m². We are asked to find the width of the box, \(x\). ## Step 2: We can rearrange the formula for pressure to solve for area. The rearranged formula is: ### \(\textbf{Area} = \frac{\textbf{Force}}{\textbf{Pressure}}\) Substituting the given values into the formula, we get: ### \(Area = \frac{27 \, \text{newtons}}{30 \, \text{newtons/m}²} = 0.9 \, \text{m}²\) ## Step 3: The area of the face of the box in contact with the table is given by the product of its length and width (1.2m and \(x\) respectively). Therefore, we can set up the equation: ### \(1.2m \cdot x = 0.9 \, \text{m}²\) Solving for \(x\), we get: ### \(x = \frac{0.9 \, \text{m}²}{1.2m} = 0.75m\)

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