Find the height $h$ of a cone if radius $r = 5 cm$ and volume $V = 100 cm$ .

Answer

$4.3702$

Explanation

To find height $h$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $V = 100 cm$ and $r = 5 cm$ we have:

100 cm = \frac{h ^{2} \cdot ( 5 cm ) ^{4} \cdot π}{3}

100 cm \cdot 3 = h^{2} \cdot (5 cm)^{4} \cdot π

300 cm = 5 cm \cdot h^{2} \cdot π

h^{2} = \frac{300 cm}{5 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=5cm and volume V=100cm.

4.3702

Find the height $h$ of a cone if radius $r = 5 cm$ and volume $V = 100 cm$ .

$4.3702$