Find the volume $V$ of a pyramid if side $a = 6 cm$ and slant height $s = 9 cm$ .

Answer

$722 cm^{3}$

Explanation

STEP 1: find height $h$

To find height $h$ use Pythagorean Theorem:

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

After substituting $a = 6 cm$ and $s = 9 cm$ we have:

h^{2} + \frac{( 6 cm ) ^{2}}{4} = (9 cm)^{2}

h^{2} + \frac{36 cm ^{2}}{4} = (9 cm)^{2}

h^{2} + 9 cm^{2} = (9 cm)^{2}

h^{2} = 81 cm^{2} - 9 cm^{2}

h^{2} = 72 cm^{2}

h = 72 cm^{2}

h = 62 cm

STEP 2: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 6 cm$ and $h = 62 cm$ we have:

V = \frac{36 cm ^{2} \cdot 6 2 cm}{3}

V = \frac{216 2 cm ^{3}}{3}

V = 722 cm^{3}

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Find the volume V of a pyramid if side a=6cm and slant height s=9cm.

722​cm3

Find the volume $V$ of a pyramid if side $a = 6 cm$ and slant height $s = 9 cm$ .

$722 cm^{3}$