Find the height $h$ of a triangular prism if volume $V = 1500 cm$ and base area $B = 250 cm$ .

Answer

$20.809$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

B = \frac{3 \cdot a ^{2}}{4}

After substituting $B = 250 cm$ we have:

250 cm = \frac{3 \cdot a ^{2}}{4}

250 cm \cdot 4 = 3 \cdot a^{2}

1000 cm = 3 \cdot a^{2}

a^{2} = \frac{1000 cm}{3}

a^{2} = \frac{1000 3}{3} cm

a = \frac{1000 3}{3} cm

a \approx 24.0281

STEP 2: find height $h$

To find height $h$ use formula:

h = \frac{3 \cdot a}{2}

After substituting $a = 24.0281 cm^{0}$ we have:

h = \frac{3 \cdot 24.0281}{2}

h = \frac{41.6179}{2}

h \approx 20.809

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Find the height h of a triangular prism if volume V=1500cm and base area B=250cm.

20.809

Find the height $h$ of a triangular prism if volume $V = 1500 cm$ and base area $B = 250 cm$ .

$20.809$