Question

if volume of sphere surface of sphere are equal in magnitude find the radius

Answer 1

Hi friend ✋✋✋✋
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Your answer
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Given that : - Volume of a sphere = Surface area of the sphere

Then, radius = ?

Now,
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$volume \: of \: sphere \: = surface \: area \: \: of \: sphere \\ \\ = > \frac{4}{3} \times \pi \times (r) {}^{3} = 4 \times \pi \times ( r) {}^{2} \\ \\ = > \frac{4}{3} \times r = 4 \\ \\ = > r = 4 \times \frac{3}{4} \\ \\ = > r \: = 3 \: units \:$
HOPE IT HELPS

Answer 2

Thus by equating the volume and surface area we can find the radius

$\frac{4}{3} \pi {r}^{3} = 4\pi {r}^{2} \\ {r}^{3} = 3 {r}^{2}$
Hence r can be (mathematically) 0 or 3, but since we are not talking about a point sphere, the radius cannot be 0.

Hence the radius is 3 units.