Find the slant height $s$ of a pyramid if height $h = 8.6 cm$ and base radius $r = 5.7 cm$ .

Answer

$10.3175 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

r = \frac{a}{2}

After substituting $r = 5.7 cm$ we have:

5.7 cm = \frac{a}{2}

a = 5.7 cm \cdot 2

a = 11.4 cm

STEP 2: find slant height $s$

To find slant height $s$ use Pythagorean Theorem:

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

After substituting $h = 8.6 cm$ and $a = 11.4 cm$ we have:

(8.6 cm)^{2} + \frac{( 11.4 cm ) ^{2}}{4} = s^{2}

73.96 cm^{2} + \frac{129.96 cm ^{2}}{4} = s^{2}

73.96 cm^{2} + 32.49 cm^{2} = s^{2}

s^{2} = 106.45 cm^{2}

s = 106.45 cm^{2}

s = 10.3175 cm

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Find the slant height s of a pyramid if height h=8.6cm and base radius r=5.7cm.

10.3175cm

Find the slant height $s$ of a pyramid if height $h = 8.6 cm$ and base radius $r = 5.7 cm$ .

$10.3175 cm$