Find the height $h$ of a triangular prism if length $l = 3 cm$ and volume $V = 4.5 cm$ .

Answer

$0.9094$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

V = \frac{3 \cdot a ^{2} \cdot l}{4}

After substituting $V = 4.5 cm$ and $l = 3 cm$ we have:

4.5 cm = \frac{3 \cdot a ^{2} \cdot ( 3 cm ) ^{4}}{4}

4.5 cm \cdot 4 = 3 \cdot a^{2} \cdot (3 cm)^{4}

18 cm = 3 \cdot a^{2} \cdot (3 cm)^{4}

18 cm = 33 cm \cdot a^{2}

a^{2} = \frac{18 cm}{3 3 cm}

a^{2} \approx 1.1027

a \approx 1.1027

a \approx 1.0501

STEP 2: find height $h$

To find height $h$ use formula:

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

After substituting $a = 1.0501 cm^{0}$ we have:

h = \frac{3 \cdot 1.0501}{2}

h = \frac{1.8188}{2}

h \approx 0.9094

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Find the height h of a triangular prism if length l=3cm and volume V=4.5cm.

0.9094

Find the height $h$ of a triangular prism if length $l = 3 cm$ and volume $V = 4.5 cm$ .

$0.9094$