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If the volume and surface area of a sphere are numerically the same. Find its diameter. |
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Answer» Volume of the sphere = \(\Large \frac{4}{3} \pi r^{3}\ cm^{3} \) Surface area of sphere = \(\Large 4 \pi r^{2}\ cm^{2}\) The volume of the sphere and the surface area of the sphere are numerically equal (given), \(\Large \frac{4}{3} \pi r^{3}\ cm^{3} \) = \(\Large 4 \pi r^{2}\ cm^{2}\) r = 3. Hence, diameter = 2r = 6cm. ATQ, Volume of sphere = SA of sphere 4/3 πr^3 = 4πr^2 => r = 3 D = 2r D = 2x3 D = 6 units 4/3πr³=4πr² 4/3r=4 r=3 therefore, diameter=3×2=6
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