Find the volume $V$ of a pyramid if side $a = 12 cm$ and slant height $s = 11 cm$ .

Answer

$4885 cm^{3}$

Explanation

STEP 1: find height $h$

To find height $h$ use Pythagorean Theorem:

h^{2} + \frac{a ^{2}}{4} = s^{2}

After substituting $a = 12 cm$ and $s = 11 cm$ we have:

h^{2} + \frac{( 12 cm ) ^{2}}{4} = (11 cm)^{2}

h^{2} + \frac{144 cm ^{2}}{4} = (11 cm)^{2}

h^{2} + 36 cm^{2} = (11 cm)^{2}

h^{2} = 121 cm^{2} - 36 cm^{2}

h^{2} = 85 cm^{2}

h = 85 cm^{2}

h = 85 cm

STEP 2: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 12 cm$ and $h = 85 cm$ we have:

V = \frac{144 cm ^{2} \cdot 85 cm}{3}

V = \frac{144 85 cm ^{3}}{3}

V = 4885 cm^{3}

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Find the volume V of a pyramid if side a=12cm and slant height s=11cm.

4885​cm3

Find the volume $V$ of a pyramid if side $a = 12 cm$ and slant height $s = 11 cm$ .

$4885 cm^{3}$