Find the volume $V$ of a pyramid if slant height $s = 9.7 cm$ and base area $B = 169 cm$ .

Answer

$405.6 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

After substituting $B = 169 cm$ we have:

B = a^{2}

a^{2} = 169 cm

a = 169 cm

a = 13

STEP 2: find height $h$

To find height $h$ use Pythagorean Theorem:

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

After substituting $a = 13 cm^{0}$ and $s = 9.7 cm$ we have:

h^{2} + \frac{13}{4} = (9.7 cm)^{2}

h^{2} + \frac{169}{4} = (9.7 cm)^{2}

h^{2} + \frac{169}{4} = (9.7 cm)^{2}

h^{2} = 94.09 cm^{2} - \frac{169}{4}

h^{2} = 51.84 cm^{2}

h = 51.84 cm^{2}

h = 7.2 cm

STEP 3: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 13 cm^{0}$ and $h = 7.2 cm$ we have:

V = \frac{169 \cdot 7.2 cm}{3}

V = \frac{1216.8 cm}{3}

V = 405.6 cm

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Find the volume V of a pyramid if slant height s=9.7cm and base area B=169cm.

405.6cm

Find the volume $V$ of a pyramid if slant height $s = 9.7 cm$ and base area $B = 169 cm$ .

$405.6 cm$