A box in the shape of a cuboid is placed on a horizontal floor. The box exerts a force of 180 newtons on the floor. The box exerts a pressure of 187.5 newtons/m² on the floor. The face in contact with the floor is a rectangle of length 1.2 metres and width x metres. Work out the value of x.

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A box in the shape of a cuboid is placed on a horizontal floor - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 2

Question 10

A box in the shape of a cuboid is placed on a horizontal floor. The box exerts a force of 180 newtons on the floor. The box exerts a pressure of 187.5 newtons/m² on... show full transcript

Worked Solution & Example Answer:A box in the shape of a cuboid is placed on a horizontal floor - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 2

Step 1

Step 1: Find the Area

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Answer

To find the area of the face in contact with the floor, we use the formula for pressure:

ext{Pressure} = rac{ ext{Force}}{ ext{Area}}

We rearrange this to find the area:

ext{Area} = rac{ ext{Force}}{ ext{Pressure}} = rac{180 ext{ N}}{187.5 ext{ N/m}^2}

Calculating this gives:

ext{Area} ext{ } ext{ } = 0.96 ext{ m}^2

Step 2

Step 2: Find the Width (x)

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Answer

We know that the area of a rectangle is given by the formula:

ext{Area} = ext{Length} imes ext{Width}

Substituting the known values:

0.96 = 1.2 imes x

To find x, rearrange this equation:

x = rac{0.96}{1.2}

Calculating x results in:

x = 0.8 ext{ m}

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