Find the diameter $d$ of a cone if height $h = 13 cm$ and volume $V = 510 cm$ .

Answer

$5.7635 cm^{-} 1$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $V = 510 cm$ and $h = 13 cm$ we have:

510 cm = \frac{13 cm ^{2} \cdot r \cdot π}{3}

510 cm \cdot 3 = 13 cm^{2} \cdot r \cdot π

1530 cm = 169 cm^{2} \cdot r \cdot π

r = \frac{1530 cm}{169 cm ^{2} π}

r = 2.8817 cm^{-} 1

STEP 2: find diameter $d$

To find diameter $d$ use formula:

d = 2 \cdot r

After substituting $r = 2.8817 cm^{-} 1$ we have:

d = 2 \cdot 2.8817 cm^{-} 1

d \approx 5.7635 cm^{-} 1

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Find the diameter d of a cone if height h=13cm and volume V=510cm.

5.7635cm−1

Find the diameter $d$ of a cone if height $h = 13 cm$ and volume $V = 510 cm$ .

$5.7635 cm^{-} 1$