Find the volume $V$ of a sphere if area $A = 200.96 cm$ .

Answer

$85.2682 π$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

A = 4 \cdot r^{2} \cdot π

After substituting $A = 200.96 cm$ we have:

200.96 cm = 4 \cdot r^{2} \cdot π

r^{2} \cdot π = \frac{200.96 cm}{4}

r^{2} \cdot π = 50.24 cm

r = \frac{50.24 cm}{π}

r \approx 3.999

STEP 2: find volume $V$

To find volume $V$ use formula:

V = \frac{4 \cdot r ^{3} \cdot π}{3}

After substituting $r = 3.999 cm^{0}$ we have:

V = \frac{4 \cdot 3.999 \cdot π}{3}

V = \frac{4 \cdot 63.9511 \cdot π}{3}

V = \frac{255.8045 \cdot π}{3}

V = 85.2682 \cdot π

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Find the volume V of a sphere if area A=200.96cm.

85.2682π

Find the volume $V$ of a sphere if area $A = 200.96 cm$ .

$85.2682 π$