Question

If the volume and surface area of a sphere are equal then calculate it's radius.​

Answer 1

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${\huge{\purple{\mathbb{\bold{ANSWER}}}}}$

${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎ Surface area of sphere = Its Volume.

▪︎ Let the radius of sphere be 'r'

${\large{\blue{\bold{\underline{Acc.\:To\:Que.:-}}}}}$

=》 4×pie×r² = 4/3×pie×r³.

=》 4r² = 4/3r³.

=》 4 = 4/3 r.

=》 4(3) = 4r.

=》 12 = 4r.

=》 r = 12/4.

${\large{\green{\boxed{\bold{=》\:r\:=\:3..}}}}}$

Therefore the radius of the sphere is 3m.

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Answer 2

AnswEr:

$\underline{\bigstar\:\textsf{Radius \: of \: Sphere \: is:}} \\\\\normalsize\ : \implies\sf\ Volume \: of \: sphere = Surface \: area \: of \: sphere \\\\\\\normalsize\ : \implies\sf\ \frac{4}{3} \pi r^{3} = 4 \pi r^{2}\\\\\\\normalsize\ : \implies\sf\ \frac{4}{3} \times\ \pi \times\ (r)^2 \times\ r = 4 \times\ \pi \times\ (r)^2 \\\\\\\normalsize\ : \implies\sf\ \frac{4}{3} \times\ \cancel{\pi} \times\ \cancel{(r^2)} \times\ r = 4 \times\ \cancel{\pi} \times\ \cancel{(r)^2} \\\\\\\normalsize\ : \implies\sf\ \frac{4}{3} \times\ r = 4\\\\\\\normalsize\ : \implies\sf\ r = 4 \times\ \frac{3}{4}\\\\\\\normalsize\ : \implies\sf\ r = \frac{12}{4}\\\\\\\normalsize\ : \implies\sf\ r = \frac{\cancel{12}}{\cancel{4}}\\\\\\\normalsize\ : \implies{\underline{\boxed{\bf{r = 3}}}}\\\\\therefore\:\underline{\textsf{The \: Radius \: of \: Sphere \: is}{\textbf{\:3 \: units}}}$