Find the volume $V$ of a sphere if area $A = 144 π cm$ .

Answer

$288 π$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

A = 4 \cdot r^{2} \cdot π

After substituting $A = 144 π cm$ we have:

144 π cm = 4 \cdot r^{2} \cdot π

r^{2} \cdot π = \frac{144 π cm}{4}

r^{2} \cdot π = 36 π cm

r^{2} = 36

r = 36

r = 6

STEP 2: find volume $V$

To find volume $V$ use formula:

V = \frac{4 \cdot r ^{3} \cdot π}{3}

After substituting $r = 6 cm^{0}$ we have:

V = \frac{4 \cdot 6 \cdot π}{3}

V = \frac{4 \cdot 216 \cdot π}{3}

V = \frac{864 \cdot π}{3}

V = 288 \cdot π

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Find the volume V of a sphere if area A=144πcm.

288π

Find the volume $V$ of a sphere if area $A = 144 π cm$ .

$288 π$