A truck is used to transport some wood panels. Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm. The density of each wood panel is 750 kg/m³. The truck can carry 15 tonnes of these wood panels. Calculate the maximum number of wood panels that the truck can carry. Show how you decide.

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A truck is used to transport some wood panels - OCR - GCSE Maths - Question 6 - 2020 - Paper 6

Question 6

A truck is used to transport some wood panels. Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm. The density of each wood panel is 750 kg/m³. The truc... show full transcript

Worked Solution & Example Answer:A truck is used to transport some wood panels - OCR - GCSE Maths - Question 6 - 2020 - Paper 6

Step 1

Calculate the volume of one wood panel

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Answer

To begin with, we need to compute the volume of a single wood panel. The dimensions of the panel are given as 2.4 m (length) by 1.2 m (width) by 1.8 cm (height). First, convert the height from centimeters to meters:

Height = 1.8 cm = 0.018 m.

Now, calculate the volume using the formula for the volume of a cuboid:

$V = ext{length} imes ext{width} imes ext{height}$

Substituting in the values, we have:

$V = 2.4 imes 1.2 imes 0.018 = 0.05184 ext{ m}^3$

Step 2

Calculate the mass of one wood panel

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Next, we can determine the mass of one wood panel using its density and the volume we just calculated. The formula relating mass, density, and volume is:

$ext{mass} = ext{density} imes ext{volume}$

Given that the density is 750 kg/m³, we get:

$ext{mass} = 750 ext{ kg/m}³ imes 0.05184 ext{ m}^3 = 38.88 ext{ kg}$

Step 3

Determine the maximum number of panels the truck can carry

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Answer

Now, since the truck can carry a total of 15 tonnes, we first convert tonnes to kilograms:

15 tonnes = 15000 kg.

To find the maximum number of wood panels the truck can carry, we divide the total weight the truck can carry by the mass of one wood panel:

$ext{max panels} = rac{ ext{total mass (kg)}}{ ext{mass of one panel (kg)}} = rac{15000}{38.88} \\ \approx 385.25$

Since we cannot have a fraction of a panel, we round down to get a total of 385 panels.

A truck is used to transport some wood panels - OCR - GCSE Maths - Question 6 - 2020 - Paper 6

Worked Solution & Example Answer:A truck is used to transport some wood panels - OCR - GCSE Maths - Question 6 - 2020 - Paper 6

Calculate the volume of one wood panel

Calculate the mass of one wood panel

Determine the maximum number of panels the truck can carry

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