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A solid metal sphere has mass 235 g - OCR - GCSE Maths - Question 12 - 2021 - Paper 1

Question 12

A solid metal sphere has mass 235 g. The density of the metal is 7.78 g/cm³. Show that the surface area of this sphere is 46.9 cm², correct to 3 significant figures... show full transcript

Worked Solution & Example Answer:A solid metal sphere has mass 235 g - OCR - GCSE Maths - Question 12 - 2021 - Paper 1

Step 1

Calculate the volume of the sphere

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Answer

Using the formula for density, we can find the volume of the sphere:

[ Density = \frac{Mass}{Volume} \implies Volume = \frac{Mass}{Density} ]

Substituting the values:

[ Volume = \frac{235 , g}{7.78 , g/cm³} \approx 30.17 , cm³ ]

Step 2

Determine the radius of the sphere

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Answer

Using the volume formula for a sphere:

[ Volume = \frac{4}{3} \pi r^3 ]

We rearrange to find r:

[ r^3 = \frac{3 \times Volume}{4 \pi} ]

Substituting the volume we found:

[ r^3 = \frac{3 \times 30.17}{4 \pi} \approx 7.17 ]

Taking the cube root results in:

[ r \approx 1.93 , cm ]

Step 3

Calculate the surface area of the sphere

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Answer

Using the surface area formula for a sphere:

[ Surface \ Area = 4 \pi r^2 ]

Substituting the radius:

[ Surface \ Area = 4 \pi (1.93)^2 \approx 46.9 , cm² ]

Thus, the surface area of the sphere is 46.9 cm², correct to 3 significant figures.

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