GCSE OCR Maths Volume: Two cylinders, A and B, are math

Two cylinders, A and B, are mathematically similar - OCR - GCSE Maths - Question 19 - 2018 - Paper 4

Question 19

Two cylinders, A and B, are mathematically similar. Cylinder A has volume 2400 cm³ and height 12 cm. Cylinder B has volume 750 cm³. Find the height of cylinder B. ... show full transcript

Worked Solution & Example Answer:Two cylinders, A and B, are mathematically similar - OCR - GCSE Maths - Question 19 - 2018 - Paper 4

Step 1

Find the scale factor for the volumes

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Answer

Since the cylinders are similar, the ratio of the volumes is equal to the cube of the ratio of corresponding linear dimensions. Let the height of cylinder B be denoted as 'h'. We know the volumes of both cylinders:

Volume of A = 2400 cm³ Volume of B = 750 cm³

Thus, we can set up the ratio as follows:

[ \frac{V_A}{V_B} = \left( \frac{h_A}{h_B} \right)^3 ] [ \frac{2400}{750} = \left( \frac{12}{h} \right)^3 ]

Step 2

Calculate the cubic ratio

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Answer

Calculating the volume ratio gives:

[ \frac{2400}{750} = 3.2 ]

This leads us to:

[ 3.2 = \left( \frac{12}{h} \right)^3 ]

We take the cube root:

[ \sqrt[3]{3.2} = \frac{12}{h} ]

Step 3

Solve for h

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Answer

Now, calculating (\sqrt[3]{3.2}):

[ \sqrt[3]{3.2} \approx 1.466 ]

Substituting back, we have:

[ 1.466 = \frac{12}{h} ]

Rearranging gives:

[ h = \frac{12}{1.466} \approx 8.17 \text{ cm} ]

Step 4

Present the final answer

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Answer

The height of cylinder B is approximately 8.17 cm, which can be rounded appropriately to 8.2 cm when considering significant figures.

Two cylinders, A and B, are mathematically similar - OCR - GCSE Maths - Question 19 - 2018 - Paper 4

Worked Solution & Example Answer:Two cylinders, A and B, are mathematically similar - OCR - GCSE Maths - Question 19 - 2018 - Paper 4

Find the scale factor for the volumes

Calculate the cubic ratio

Solve for h

Present the final answer

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