Find the lateral edge $e$ of a pyramid if slant height $s = 68.479 cm$ and base radius $r = 45.822 cm$ .

Answer

$82.3956 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

r = \frac{a}{2}

After substituting $r = 45.822 cm$ we have:

45.822 cm = \frac{a}{2}

a = 45.822 cm \cdot 2

a = 91.644 cm

STEP 2: find lateral edge $e$

To find lateral edge $e$ use Pythagorean Theorem:

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

After substituting $s = 68.479 cm$ and $a = 91.644 cm$ we have:

(68.479 cm)^{2} + \frac{( 91.644 cm ) ^{2}}{4} = e^{2}

4689.3734 cm^{2} + \frac{8398.6227 cm ^{2}}{4} = e^{2}

4689.3734 cm^{2} + 2099.6557 cm^{2} = e^{2}

e^{2} = 6789.0291 cm^{2}

e = 6789.0291 cm^{2}

e = 82.3956 cm

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Find the lateral edge e of a pyramid if slant height s=68.479cm and base radius r=45.822cm.

82.3956cm

Find the lateral edge $e$ of a pyramid if slant height $s = 68.479 cm$ and base radius $r = 45.822 cm$ .

$82.3956 cm$