Find the length $l$ of a triangular prism if height $h = 11 cm$ and volume $V = 115.5 cm$ .

Answer

$1.6533 cm^{-} 1$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $h = 11 cm$ we have:

11 cm = \frac{3 \cdot a}{2}

3 \cdot a = 11 cm \cdot 2

3 \cdot a = 22 cm

a = \frac{22 cm}{3}

a = \frac{22 3}{3} cm

STEP 2: find length $l$

To find length $l$ use formula:

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

After substituting $V = 115.5 cm$ and $a = \frac{22 3}{3} cm$ we have:

115.5 cm = \frac{3 \cdot \frac{22 3}{3} cm ^{2} \cdot l}{4}

115.5 cm \cdot 4 = 3 \cdot \frac{22 3}{3} cm^{2} \cdot l

462 cm = 3 \cdot \frac{22 3}{3} cm^{2} \cdot l

462 cm = \frac{484 3}{3} cm^{2} \cdot l

l = \frac{462 cm}{\frac{484 3}{3} cm ^{2}}

l = 1.6533 cm^{-} 1

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Find the length l of a triangular prism if height h=11cm and volume V=115.5cm.

1.6533cm−1

Find the length $l$ of a triangular prism if height $h = 11 cm$ and volume $V = 115.5 cm$ .

$1.6533 cm^{-} 1$