Question
Find the volume of a sphere whose surface area is $154 cm^2$.
✓
Answer
Let the radius of the sphere be $r cm.$
Surface area = $154 cm^2$
$\Rightarrow\ 4\pi r^2$ = 154
$\Rightarrow\ 4\times{22\over7}\times r^2=154$
$\Rightarrow\ r^2={154\times7\over4\times22}\Rightarrow {r^2={49\over4} }$
$\Rightarrow r=\sqrt{49\over4}\Rightarrow r={7\over2}$ cm
$\therefore$Volume of the sphere =${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times({7\over2})^2={539\over3}\ cm^3$
$=179{2\over3}\ cm^3$
Surface area = $154 cm^2$
$\Rightarrow\ 4\pi r^2$ = 154
$\Rightarrow\ 4\times{22\over7}\times r^2=154$
$\Rightarrow\ r^2={154\times7\over4\times22}\Rightarrow {r^2={49\over4} }$
$\Rightarrow r=\sqrt{49\over4}\Rightarrow r={7\over2}$ cm
$\therefore$Volume of the sphere =${4\over3}\pi r^3$
$={4\over3}\times{22\over7}\times({7\over2})^2={539\over3}\ cm^3$
$=179{2\over3}\ cm^3$
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