Find the volume $V$ of a pyramid if side $a = 8 cm$ and lateral edge $e = 8 cm$ .

Answer

$\frac{256 2}{3} cm^{3}$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use formula:

d = 2 \cdot a

After substituting $a = 8 cm$ we have:

d = 2 \cdot 8 cm

d = 82 cm

STEP 2: find height $h$

To find height $h$ use Pythagorean Theorem:

h^{2} + \frac{d ^{2}}{4} = e^{2}

After substituting $d = 82 cm$ and $e = 8 cm$ we have:

h^{2} + \frac{( 8 2 cm ) ^{2}}{4} = (8 cm)^{2}

h^{2} + \frac{128 cm ^{2}}{4} = (8 cm)^{2}

h^{2} + 32 cm^{2} = (8 cm)^{2}

h^{2} = 64 cm^{2} - 32 cm^{2}

h^{2} = 32 cm^{2}

h = 32 cm^{2}

h = 42 cm

STEP 3: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 8 cm$ and $h = 42 cm$ we have:

V = \frac{64 cm ^{2} \cdot 4 2 cm}{3}

V = \frac{256 2 cm ^{3}}{3}

V = \frac{256 2}{3} cm^{3}

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Find the volume V of a pyramid if side a=8cm and lateral edge e=8cm.

32562​​cm3

Find the volume $V$ of a pyramid if side $a = 8 cm$ and lateral edge $e = 8 cm$ .

$\frac{256 2}{3} cm^{3}$