Find the height $h$ of a cone if diameter $d = 8 cm$ and slant height $l = 17 cm$ .

Answer

$273 cm$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

d = 2 \cdot r

After substituting $d = 8 cm$ we have:

8 cm = 2 \cdot r

r = \frac{8 cm}{2}

r = 4 cm

STEP 2: find side $h$

To find side $h$ use Pythagorean Theorem:

r^{2} + h^{2} = l^{2}

After substituting $r = 4 cm$ and $l = 17 cm$ we have:

(4 cm)^{2} + h^{2} = (17 cm)^{2}

h^{2} = (17 cm)^{2} - (4 cm)^{2}

h^{2} = 289 cm^{2} - 16 cm^{2}

h^{2} = 273 cm^{2}

h = 273 cm^{2}

h = 273 cm

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Find the height h of a cone if diameter d=8cm and slant height l=17cm.

273​cm

Find the height $h$ of a cone if diameter $d = 8 cm$ and slant height $l = 17 cm$ .

$273 cm$