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The diagram shows a cylinder and a sphere - OCR - GCSE Maths - Question 6 - 2018 - Paper 4

Question 6

The diagram shows a cylinder and a sphere. The cylinder has radius 12 cm and height 30 cm. The cylinder and the sphere have the same volume. Work out the radius rc... show full transcript

Worked Solution & Example Answer:The diagram shows a cylinder and a sphere - OCR - GCSE Maths - Question 6 - 2018 - Paper 4

Step 1

Find the volume of the cylinder

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Answer

The volume V of a cylinder can be calculated using the formula:

$V = \pi r^2 h$

Substituting the values for the radius (r = 12 cm) and height (h = 30 cm):

$V = \pi (12)^2 (30) = \pi (144)(30) = 4320\pi \text{ cm}^3$

Step 2

Set the volume of the sphere equal to the volume of the cylinder

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Answer

Since the volumes of the cylinder and sphere are equal, we set:

$\frac{4}{3} \pi r_{cm}^3 = 4320\pi$

Dividing both sides by (\pi):

$\frac{4}{3} r_{cm}^3 = 4320$

Step 3

Solve for rcm

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Answer

Multiplying both sides by (\frac{3}{4}):

$r_{cm}^3 = 4320 \times \frac{3}{4} = 3240$

Now take the cube root:

$r_{cm} = \sqrt[3]{3240} \approx 14.79 \text{ cm}$

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