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Answer 1 · 2017-03-07T08:25:15

The height of the cone ( $h$ $h$ ) is $6$ $6$ .

Explanation:

Sure, Nissa, This one is quite easy.

The height ( $h$ $h$ ) of the cone, the radius ( $r = \frac{d}{2} = \frac{16}{2} = 8$ $r=d/2=16/2=8$ ) of the base of the cone and the length ( $l = 10$ $l=10$ )of the side of the cone form the three sides of a right-angled triangle with $l$ $l$ as the hypotenuse.

According to the Pythagorean theorem, the sum of the squares of the two sides of the right angle equals the square of the hypotenuse.

Hence:

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

Since we know that $r = 8$ $r=8$ and $l = 10$ $l=10$ ,

$h^{2} + 8^{2} = 10^{2}$ $h^2+8^2=10^2$

$h^{2} + 64 = 100$ $h^2+64=100$

Subtract $64$ $64$ from both sides.

$h^{2} = 100 - 64$ $h^2=100-64$

$h^{2} = 36$ $h^2=36$

$h = \sqrt{36}$ $h=sqrt36$

$h = 6$ $h=6$

Hence the height of the cone ( $h$ $h$ ) is $6$ $6$ .

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