A capsule of medicine is in the shape of a sp | vedclass

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Question

(A) The diameter of the spherical capsule is $d = 3.5 \, mm$.The radius $r$ of the capsule is given by $r = \frac{d}{2} = \frac{3.5}{2} = 1.75 \, mm$.

Vedclass · Accepted Answer

$22.46$

Vedclass · Answer

(A) The diameter of the spherical capsule is $d = 3.5 \, mm$.The radius $r$ of the capsule is given by $r = \frac{d}{2} = \frac{3.5}{2} = 1.75 \, mm$.The volume $V$ of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Substituting the values,we get:$V = \frac{4}{3} 	imes \frac{22}{7} 	imes (1.75)^3 \, mm^3$$V = \frac{4}{3} 	imes \frac{22}{7} 	imes \left(\frac{7}{4}ight)^3 \, mm^3$$V = \frac{4}{3} 	imes \frac{22}{7} 	imes \frac{7 	imes 7 	imes 7}{4 	imes 4 	imes 4} \, mm^3$$V = \frac{22 	imes 7 	imes 7}{3 	imes 4 	imes 4} \, mm^3 = \frac{1078}{48} \, mm^3 \approx 22.4583 \, mm^3$.Rounding to two decimal places,the volume is approximately $22.46 \, mm^3$.

$A$ capsule of medicine is in the shape of a sphere of diameter $3.5 \, mm$. How much medicine (in $mm^3$) is needed to fill this capsule (in $, mm^3$)?

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