Find the height $h$ of a cone if volume $V = 198 cm$ and base area $A B = 22 cm$ .

Answer

$8.4528$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

After substituting $A B = 22 cm$ we have:

A B = r^{2} \cdot π

r^{2} \cdot π = 22 cm

r = \frac{22 cm}{π}

r \approx 2.6463

STEP 2: find height $h$

To find height $h$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $V = 198 cm$ and $r = 2.6463 cm^{0}$ we have:

198 cm = \frac{h ^{2} \cdot 2.6463 \cdot π}{3}

198 cm \cdot 3 = h^{2} \cdot 2.6463 \cdot π

594 cm = 2.6463 \cdot h^{2} \cdot π

h^{2} = \frac{594 cm}{2.6463 π}

h^{2} \approx 71.4496 cm

h \approx 71.4496 cm

h \approx 8.4528

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Find the height h of a cone if volume V=198cm and base area AB=22cm.

8.4528

Find the height $h$ of a cone if volume $V = 198 cm$ and base area $A B = 22 cm$ .

$8.4528$