Question

Can you help me with this question.?

My teacher requires work if it is not too much of a hassle please SHOW WORK!!!! thank you for helping.

Answer 1

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

Explanation:

Sure, Nissa, This one is quite easy.

The height (`h`) of the cone, the radius (`r=d/2=16/2=8`) of the base of the cone and the length (`l=10`)of the side of the cone form the three sides of a right-angled triangle with `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`

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

`h^2+8^2=10^2`

`h^2+64=100`

Subtract `64` from both sides.

`h^2=100-64`

`h^2=36`

`h=sqrt36`

`h=6`

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