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.

GCSE OCR Maths Sin, Cos, Tan: A truck is used to transport som

A truck is used to transport some wood panels - OCR - GCSE Maths - Question 18 - 2020 - Paper 3

Question 18

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 18 - 2020 - Paper 3

Step 1

Calculate the volume of one wood panel

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Answer

The volume of a cuboid can be calculated using the formula:

$Volume = length \times width \times height$

First, we need to convert all dimensions to meters. The height is given as 1.8 cm, which is equivalent to 0.018 m.

Thus, the dimensions for a single wood panel are:

Length = 2.4 m
Width = 1.2 m
Height = 0.018 m

Now, substituting these values into the volume formula:

$Volume = 2.4 \times 1.2 \times 0.018 = 0.05184 \ m^3$

Step 2

Calculate the mass of one wood panel

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Answer

To find the mass of a wood panel, we use the formula:

$Mass = Volume \times Density$

We already calculated the volume as 0.05184 m³ and the density is 750 kg/m³.

Substituting these values:

$Mass = 0.05184 \times 750 = 38.88 \ kg$

Step 3

Calculate the total mass the truck can carry

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Answer

The truck can carry 15 tonnes, which is equivalent to:

$15 \ tonnes = 15000 \ kg$

Step 4

Calculate the maximum number of wood panels the truck can carry

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Answer

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

$Number \ of \ Panels = \frac{Total \ Mass}{Mass \ of \ One \ Panel}$

Substituting the values:

$Number \ of \ Panels = \frac{15000 \ kg}{38.88 \ kg} \approx 385.5$

Since the truck cannot carry a fraction of a panel, we take the whole number:

Maximum number of wood panels = 385

A truck is used to transport some wood panels - OCR - GCSE Maths - Question 18 - 2020 - Paper 3

Worked Solution & Example Answer:A truck is used to transport some wood panels - OCR - GCSE Maths - Question 18 - 2020 - Paper 3

Calculate the volume of one wood panel

Calculate the mass of one wood panel

Calculate the total mass the truck can carry

Calculate the maximum number of wood panels the truck can carry

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