Question

The volume of a sphere varies directly with cube of length of its radius and surface area of sphere varies directly with the square of the length of the radius. let us prove that the square of volume of sphere varies directly with the cube of its surface area.​

Answer 1

EXAPLAINATION:-

$let \: us \: the \: radius \: be \: = r \\ then \\ th \: volume \: of \: the \: given \: sphere \: is \: 36\pi {r}^{3} \\ the \: volume \: \: of \: every \: sphere \: is \: \\ v = \frac{4}{3} \pi {r}^{3} \\ \\ \\ some \: can \: equate \: the \: two \: volume \\ 36\pi = \frac{4}{3} \pi {r}^{3} \\ both \: side \: multiply \: 3 \\ 36\pi \times 3 = \frac{4}{3} \pi {r}^{3} \times 3 \\ 108\pi = 4\pi {r}^{3} \\ \frac{108\pi}{4\pi} = {r}^{3} \\ 27 = {r}^{3} \\ 3 = r$

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