Find the volume $V$ of a pyramid if height $h = 100000 cm$ and lateral edge $e = 116000 cm$ .

Answer

$2.304 E + 14 cm^{3}$

Explanation

STEP 1: find base diagonal $d$

To find base diagonal $d$ use Pythagorean Theorem:

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

After substituting $h = 100000 cm$ and $e = 116000 cm$ we have:

(100000 cm)^{2} + \frac{d ^{2}}{4} = (116000 cm)^{2}

\frac{d ^{2}}{4} = (116000 cm)^{2} - (100000 cm)^{2}

\frac{d ^{2}}{4} = 13456000000 cm^{2} - 10000000000 cm^{2}

d^{2} = 3456000000 cm^{2} \cdot 4

d^{2} = 13824000000 cm^{2}

d = 13824000000 cm^{2}

d = 480006 cm

STEP 2: find side $a$

To find side $a$ use formula:

d = 2 \cdot a

After substituting $d = 480006 cm$ we have:

480006 cm = 2 \cdot a

a = \frac{48000 6 cm}{2}

a = 480003 cm

STEP 3: find volume $V$

To find volume $V$ use formula:

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

After substituting $a = 480003 cm$ and $h = 100000 cm$ we have:

V = \frac{6912000000 cm ^{2} \cdot 100000 cm}{3}

V = \frac{6.912 E + 14 cm ^{3}}{3}

V = 2.304 E + 14 cm^{3}

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Find the volume V of a pyramid if height h=100000cm and lateral edge e=116000cm.

2.304E+14cm3

Find the volume $V$ of a pyramid if height $h = 100000 cm$ and lateral edge $e = 116000 cm$ .

$2.304 E + 14 cm^{3}$