Question

Qual volume de uma esfera de 5.000 km de diâmetro?

Answer 1

O volume de uma esfera é dado por $V=(4/3)*\pi*r^{3}$

$d = 5000km$
$2r=5000$
$r=5000/2$
$r=2500km$
$r=25*10^{2}km$

$V=(4/3)*\pi*r^{3} \\ V=(4/3)*\pi*(25*10^{2})^{3} \\V= (4/3)*\pi*25^{3}*(10^{2})^{3}$
$V=(4/3)*\pi*15625*10^{6}$
$V=62500*\pi*10^{6}/3$
$V=6,25*10^{4}*\pi*10^{6}/3$
$V=[6,25\pi*10^{10}/3]km^{3}$
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Se preferir o volume em m³, uma medida mais comum:

$r=2500km \\ r=2500*1000m \\ r=25*10^{5}m$

$V=(4/3)*\pi*(25*10^{5})^{3}$
$V=(4/3)*\pi*25^{3}*(10^{5})^{3}$
$V=(4/3)*\pi*15625*10^{15}$
$V=4*\pi*15625*10^{15}/3$
$V=62500*\pi*10^{15}/3$
$V=6,25*10^{4}*\pi*10^{15}/3$
$V=[6,25\pi*10^{19}/3]m^{3}$