A container is in the shape of a cuboid. The dimensions of the container are: - Length: 30 cm - Width: 6 cm - Height: 19 cm The container is $rac{2}{3}$ full of water. A cup holds 275 ml of water. What is the greatest number of cups that can be completely filled with water from the container?

GCSE Edexcel Maths Ratio Analysis and Problem Solving: A container is in the shape of a

A container is in the shape of a cuboid - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Question 4

A container is in the shape of a cuboid. The dimensions of the container are: - Length: 30 cm - Width: 6 cm - Height: 19 cm The container is $rac{2}{3}$ full of... show full transcript

Worked Solution & Example Answer:A container is in the shape of a cuboid - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Step 1

Calculate the volume of the container

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Answer

To find the volume of the cuboid, we use the formula:

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

Substituting the given dimensions:

$V = 30 ext{ cm} imes 6 ext{ cm} imes 19 ext{ cm} = 3420 ext{ cm}^3$

Step 2

Calculate the volume of water in the container

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Answer

Since the container is $rac{2}{3}$ full of water, we calculate the volume of water as follows:

$V_{ ext{water}} = rac{2}{3} imes 3420 ext{ cm}^3 = 2280 ext{ cm}^3$

Step 3

Convert the volume of water to milliliters

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Answer

Since 1 cm³ is equivalent to 1 ml, the volume of the water in milliliters is:

$V_{ ext{water}} = 2280 ext{ ml}$

Step 4

Determine the greatest number of cups that can be filled

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Answer

To find the number of cups that can be filled, we divide the total volume of water by the volume of one cup:

$ext{Number of cups} = rac{2280 ext{ ml}}{275 ext{ ml/cup}} \\ = 8.29$

Since we can only fill whole cups, the greatest number of cups that can be completely filled is:

8 cups.

A container is in the shape of a cuboid - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Worked Solution & Example Answer:A container is in the shape of a cuboid - Edexcel - GCSE Maths - Question 4 - 2019 - Paper 2

Calculate the volume of the container

Calculate the volume of water in the container

Convert the volume of water to milliliters

Determine the greatest number of cups that can be filled

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