Find the slant height $s$ of a pyramid if height $h = 4 cm$ and base radius $r = 3 cm$ .

Answer

$5 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

r = \frac{a}{2}

After substituting $r = 3 cm$ we have:

3 cm = \frac{a}{2}

a = 3 cm \cdot 2

a = 6 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 $h = 4 cm$ and $a = 6 cm$ we have:

(4 cm)^{2} + \frac{( 6 cm ) ^{2}}{4} = s^{2}

16 cm^{2} + \frac{36 cm ^{2}}{4} = s^{2}

16 cm^{2} + 9 cm^{2} = s^{2}

s^{2} = 25 cm^{2}

s = 25 cm^{2}

s = 5 cm

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Find the slant height s of a pyramid if height h=4cm and base radius r=3cm.

5cm

Find the slant height $s$ of a pyramid if height $h = 4 cm$ and base radius $r = 3 cm$ .

$5 cm$