Find the diameter $d$ of a cone if height $h = 3 cm$ and volume $V = 12.4 cm$ .

Answer

$2.6314 cm^{-} 1$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $V = 12.4 cm$ and $h = 3 cm$ we have:

12.4 cm = \frac{3 cm ^{2} \cdot r \cdot π}{3}

12.4 cm \cdot 3 = 3 cm^{2} \cdot r \cdot π

37.2 cm = 9 cm^{2} \cdot r \cdot π

r = \frac{37.2 cm}{9 cm ^{2} π}

r = 1.3157 cm^{-} 1

STEP 2: find diameter $d$

To find diameter $d$ use formula:

d = 2 \cdot r

After substituting $r = 1.3157 cm^{-} 1$ we have:

d = 2 \cdot 1.3157 cm^{-} 1

d \approx 2.6314 cm^{-} 1

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Find the diameter d of a cone if height h=3cm and volume V=12.4cm.

2.6314cm−1

Find the diameter $d$ of a cone if height $h = 3 cm$ and volume $V = 12.4 cm$ .

$2.6314 cm^{-} 1$