Question

Q7. If the volume of a sphere is numerically equal to its surface area, then find the

diameter of the sphere.​

Answer 1

$\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

${\sf{☞ Volume \: of \: sphere \: = \: surface \: area \: of \: sphere}}$

${\sf{☞ \ \frac{4}{3} \pi {r}^{3} \: = \: 4\pi {r}^{2}}}$

$\Large{\orange{\tt{\underline{\underline{To \ find \ :-}}}}}$

${\sf{↣Diameter \: of \: sphere}}$

$\Large{\green{\tt{\underline{\underline{Solution \ :-}}}}}$

According to question

${\sf{↣ \ \frac{4}{3} \pi {r}^{3} \: = \: 4\pi {r}^{2}}}$

${\sf{↣ \ \frac{ {r}^{3} }{ {r}^{2} } \: = \: 4\pi \times \frac{3}{4} \pi}}$

${\sf{↣ \ r \: = \: 3 \: unit}}$

Hence

${\sf{↣ \ Diameter \: = \: 2 \times r}}$

${\sf{↣ \ Diameter \: = \: 6 \: unit}}$

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Hope it's help ⚓⚓

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