WBBSEClass XMathematicsSphere02 Mark2023 Moderate

QQuestion

The numerical value of the volume of a sphere is twice the numerical value of its surface area. Find the radius of the sphere.

Exam-ready answer 02 Mark

Answer

Volume of the sphere = 4\over3πr³

Surface area of the sphere = 4πr²

Given that the volume is twice the surface area:

4\over3πr³ = 2 × 4πr²

4\over3r³ = 8r²

4\over3r = 8

⇒ 4r = 24

⇒ r = 6

Thus, the radius of the sphere is 6 units.

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