Question

A princess hat for a costume is shaped like a cone. The base of the cone is 12 in across and the height is 8

in. The slant height of the outside edge, which is unknown, is the hypotenuse of the right triangle formed with
the radius and the height of the cone.
(a) Sketch the princess hat. Label the known lengths as described and label the unknown length as x.
(b) What is the slant height of the outside edge?

Answer 1

Part a) The drawn in the attached figure

Part b)The slant height of the outside edge is
`x=10\ in`

Explanation:

Part a) The drawn in the attached figure

Part b) What is the slant height of the outside edge?

we have that

The diameter of the base of the cone is 12 in

so

`r=12/2=6\ in` ----> the radius is half the diameter

`h=8\ in`

Applying the Pythagoras Theorem find the slant height x

`x^(2)=r^(2)+h^(2)`

substitute the values

`x^(2)=6^(2)+8^(2)`

`x^(2)=100`

`x=10\ in`