Question

PLEASE HELP ASAP.. WILL FAN AND MEDAL

A cone-shaped hat is shown:

A cone is shown with slant height 18 cm and radius 5.7 cm. The unknown height is labeled with a question mark, and the line joining the tip of the cone to the base is perpendicular to the base.

What is the approximate height of the hat?

3.51 centimeters, because height = Square root of the difference of 18 and 5.7
17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7
18.88 centimeters, because height = Square root of the sum of the squares of 18 and 5.7
4.87 centimeters, because height = Square root of the sum of 18 and 5.7

Answer 1

Answer: 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.

Explanation:

Given: The slant height of the cone (l)= 18 cm

The radius of the cone (r) =5.7 cm

Let h be the height of the cone .

We know that the above dimensions make aright triangle in a cone, such that by Pythagoras theorem

`l^2=h^2-r^2\\\Rightarrow\ h^2=l^2-r^2\\\Rightarrow\ h=√(l^2-r^2)\\\Rightarrow\ h=√(18^2-5.7^2)`

Thus, height = Square root of the difference of the squares of 18 and 5.7

and,

`\Rightarrow\ h=√(324-32.49)\\\Rightarrow\ h=√(291.51)\\\Rightarrow\ h=17.0736639302\approx17.07\ cm`