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A and B are two similar cylindrical containers - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 1

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A and B are two similar cylindrical containers. The surface area of container A : the surface area of container B = 4 : 9. Tyler fills container A with water. He ... show full transcript

Worked Solution & Example Answer:A and B are two similar cylindrical containers - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 1

Step 1

Find the ratio of corresponding lengths

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Answer

Since the surface area ratio of containers A and B is given as 4:9, we can deduce the ratio of their corresponding linear dimensions (lengths) by taking the square root of the ratio of the surface areas:

rac{length_A}{length_B} = rac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}.

Step 2

Find the ratio of volumes

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Answer

The volume ratio of similar shapes can be derived from the cube of the ratio of their corresponding lengths. Thus, we calculate the volume ratio as follows:

volumeAvolumeB=(lengthAlengthB)3=(23)3=827.\frac{volume_A}{volume_B} = \left(\frac{length_A}{length_B}\right)^3 = \left(\frac{2}{3}\right)^3 = \frac{8}{27}.

Step 3

Determine the number of times container A fills container B

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Answer

Let the volume of container A be 8 units (based on the volume ratio). Therefore, to fill container B (27 units), Tyler would need to fill it:

volumeBvolumeA=278=3.375.\frac{volume_B}{volume_A} = \frac{27}{8} = 3.375.

This means Tyler will fill container A a total of 4 times to reach or exceed the total volume needed for container B.

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