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A sphere has a radius of 3 cm - OCR - GCSE Maths - Question 19 - 2023 - Paper 2

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A sphere has a radius of 3 cm. Calculate the volume of the sphere. Give your answer in terms of $ p$ in its simplest form. [The volume $V$ of a sphere with radius $... show full transcript

Worked Solution & Example Answer:A sphere has a radius of 3 cm - OCR - GCSE Maths - Question 19 - 2023 - Paper 2

Step 1

Calculate the volume of the sphere

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Answer

To find the volume VV of a sphere, we use the formula: V=43Ï€r3V = \frac{4}{3} \pi r^3

Given that the radius rr is 3 cm, we substitute: V=43Ï€(3)3V = \frac{4}{3} \pi (3)^3

Calculating the radius cubed: (3)3=27(3)^3 = 27

Now substituting back into the formula: V=43π⋅27V = \frac{4}{3} \pi \cdot 27

Simplifying, we have: V=1083Ï€=36Ï€V = \frac{108}{3} \pi = 36\pi

Thus, the volume of the sphere is: V=36Ï€ cm3V = 36\pi \text{ cm}^3

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