SOLUTION: Conical clown hats with a height of 25cm will be made from circular paper. If the circumference of a clown's head is 60cm, what is the radius of the original circle from which the

Algebra ->  Circles -> SOLUTION: Conical clown hats with a height of 25cm will be made from circular paper. If the circumference of a clown's head is 60cm, what is the radius of the original circle from which the      Log On


   

Question 139715: Conical clown hats with a height of 25cm will be made from circular paper. If the circumference of a clown's head is 60cm, what is the radius of the original circle from which the hat was made? Please help me:)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The radius of the original circle needs to be the slant height of the cone. The slant height is the length of any line segment that connects the apex of the cone with any point on the perimeter of the base. The slant height is also the hypotenuse of a right triangle where one of the sides is the height of the cone and the other is a radius of the base.

So, you are given the circumference of the base, 60 cm, which we know to be equal to 2%2Api%2Ar. That means that the radius is r=60%2F%282%2Api%29=30%2Fpi

You are given the height, 25cm, so the slant height, s must be s=sqrt%28%2830%2Fpi%29%5E2%2B25%5E2%29.

Ewwww! THAT looks ugly. Looks like you have some calculator work to do.