Find the volume $V$ of a pyramid if side $a = 9 cm$ and slant height $s = 10 cm$ .

Answer

$\frac{27 319}{2} cm^{3}$

Explanation

STEP 1: find height $h$

To find height $h$ use Pythagorean Theorem:

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

After substituting $a = 9 cm$ and $s = 10 cm$ we have:

h^{2} + \frac{( 9 cm ) ^{2}}{4} = (10 cm)^{2}

h^{2} + \frac{81 cm ^{2}}{4} = (10 cm)^{2}

h^{2} + \frac{81}{4} cm^{2} = (10 cm)^{2}

h^{2} = 100 cm^{2} - \frac{81}{4} cm^{2}

h^{2} = \frac{319}{4} cm^{2}

h = \frac{319}{4} cm^{2}

h = \frac{319}{2} cm

STEP 2: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 9 cm$ and $h = \frac{319}{2} cm$ we have:

V = \frac{81 cm ^{2} \cdot \frac{319}{2} cm}{3}

V = \frac{\frac{81 319}{2} cm ^{3}}{3}

V = \frac{27 319}{2} cm^{3}

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Find the volume V of a pyramid if side a=9cm and slant height s=10cm.

227319​​cm3

Find the volume $V$ of a pyramid if side $a = 9 cm$ and slant height $s = 10 cm$ .

$\frac{27 319}{2} cm^{3}$