Find the height $h$ of a cone if radius $r = 6 cm$ and volume $V = 120 cm$ .

Answer

$4.3702$

Explanation

To find height $h$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $V = 120 cm$ and $r = 6 cm$ we have:

120 cm = \frac{h ^{2} \cdot ( 6 cm ) ^{4} \cdot π}{3}

120 cm \cdot 3 = h^{2} \cdot (6 cm)^{4} \cdot π

360 cm = 6 cm \cdot h^{2} \cdot π

h^{2} = \frac{360 cm}{6 cm π}

h^{2} \approx 19.0985

h \approx 19.0985

h \approx 4.3702

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Find the height h of a cone if radius r=6cm and volume V=120cm.

4.3702

Find the height $h$ of a cone if radius $r = 6 cm$ and volume $V = 120 cm$ .

$4.3702$